@inproceedings{RH:86,
author = {R. Hamming},
booktitle = {Bell Communications Research Colloquium Seminar},
note = {Transcripted by James F. Kaiser. (Later version of
the talk at
\url{https://www.youtube.com/watch?v=a1zDuOPkMSw})},
organization = {Bell Communications Research, Morristown, NJ},
pages = {483},
title = {You and your research},
year = {1986},
url = {http://motion.me.ucsb.edu/RHamming-YouAndYourResearch-
1986.pdf},
}
@book{RG:14,
author = {R. Ghrist},
edition = {1.0},
publisher = {Createspace},
title = {Elementary Applied Topology},
year = {2014},
isbn = {978-1502880857},
}
@article{JRPF:56,
author = {J. R. P. {French~Jr.}},
journal = {Psychological Review},
number = {3},
pages = {181--194},
title = {A formal theory of social power},
volume = {63},
year = {1956},
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}
@incollection{FH:59,
author = {F. Harary},
booktitle = {Studies in Social Power},
editor = {D. Cartwright},
pages = {168--182},
publisher = {University of Michigan},
title = {A criterion for unanimity in {F}rench's theory of
social power},
year = {1959},
isbn = {0879442301},
url = {http://psycnet.apa.org/psycinfo/1960-06701-006},
}
@article{MHDG:74,
author = {M. H. DeGroot},
journal = {Journal of the American Statistical Association},
number = {345},
pages = {118-121},
title = {Reaching a Consensus},
volume = {69},
year = {1974},
abstract = {Consider a group of individuals who must act together
as a team or committee, and suppose that each
individual in the group has his own subjective
probability distribution for the unknown value of
some parameter. A model is presented which describes
how the group might reach agreement on a common
subjective probability distribution for the parameter
by pooling their individual opinions. The process
leading to the consensus is explicitly described and
the common distribution that is reached is explicitly
determined. The model can also be applied to problems
of reaching a consensus when the opinion of each
member of the group is represented simply as a point
estimate of the parameter rather than as a
probability distribution.},
doi = {10.1080/01621459.1974.10480137},
}
@article{INM:73,
author = {I. Noy-Meir},
journal = {Annual Review of Ecology and Systematics},
pages = {25--51},
title = {Desert ecosystems. {I}. {E}nvironment and producers},
year = {1973},
doi = {10.1146/annurev.es.04.110173.000325},
}
@article{MSK-DJN:71,
author = {M. S. Klamkin and D. J. Newman},
journal = {American Mathematical Monthly},
number = {6},
pages = {631-639},
title = {Cyclic pursuit or "the three bugs problem"},
volume = {78},
year = {1971},
doi = {10.4169/amer.math.monthly.122.04.377},
}
@techreport{AMB-NC-AE:91,
address = {Haifa, Israel},
author = {A. M. Bruckstein and N. Cohen and A. Efrat},
institution = {Center for Intelligent Systems, Technion},
month = jul,
number = {CIS 9105},
title = {Ants, crickets, and frogs in cyclic pursuit},
year = {1991},
url = {http://www.cs.technion.ac.il/tech-reports},
}
@inproceedings{LX-SB-SL:05,
address = {Los Angeles, CA, USA},
author = {L. Xiao and S. Boyd and S. Lall},
booktitle = {Symposium on Information Processing of Sensor
Networks},
month = apr,
pages = {63-70},
title = {A scheme for robust distributed sensor fusion based
on average consensus},
year = {2005},
doi = {10.1109/IPSN.2005.1440896},
}
@incollection{FG-LS:10,
author = {F. Garin and L. Schenato},
booktitle = {Networked Control Systems},
editor = {A. Bemporad and M. Heemels and M. Johansson},
pages = {75-107},
publisher = {Springer},
title = {A Survey on Distributed Estimation and Control
Applications Using Linear Consensus Algorithms},
year = {2010},
doi = {10.1007/978-0-85729-033-5_3},
}
@book{VHP:98,
author = {V. H. Poor},
edition = {2},
publisher = {Springer},
title = {An Introduction to Signal Detection and Estimation},
year = {1998},
isbn = {0387941738},
}
@article{BSYR-HFDH:93,
author = {B. S. Y. Rao and H. F. Durrant-Whyte},
journal = {IEEE Transactions on Systems, Man \& Cybernetics},
number = {6},
pages = {1683-1698},
title = {A decentralized {Bayesian} algorithm for
identification of tracked targets},
volume = {23},
year = {1993},
abstract = {The problem of identification of objects being
tracked by a fully decentralized surveillance system
is considered. A decentralized multisensor system is
used to track targets (people and mobile robots) as
they enter and move around a factory assembly room
performing tasks. The sensors used in this system
(CCD cameras) reveal information about the targets
that is sufficiently rich to allow them not only to
be tracked, but also identified as a person, a robot,
etc. This identity information can be used to aid in
man-machine interface design and to facilitate
situation assessment. After defining the
identification problem, a centralized Bayesian
algorithm is developed for determining the identity
of each target based on each sensor's information.
The algorithm is decentralized and its performance
compared to the centralized version. Results of an
implementation of the algorithm working on real data
from the surveillance system are presented},
doi = {10.1109/21.257763},
}
@incollection{ROS-EF-EF-JSS:06,
author = {R. Olfati-Saber and E. Franco and E. Frazzoli and
J. S. Shamma},
booktitle = {Network Embedded Sensing and Control. (Proceedings of
NESC'05 Worskhop)},
editor = {P. J. Antsaklis and P. Tabuada},
pages = {169-182},
publisher = {Springer},
series = {Lecture Notes in Control and Information Sciences},
title = {Belief consensus and distributed hypothesis testing
in sensor networks},
year = {2006},
doi = {10.1007/11533382_11},
isbn = {3540327940},
}
@incollection{MWS-NC:07,
author = {M. W. Spong and N. Chopra},
booktitle = {Lagrangian and Hamiltonian Methods for Nonlinear
Control 2006},
pages = {47-59},
publisher = {Springer},
series = {Lecture Notes in Control and Information Sciences},
title = {Synchronization of Networked {L}agrangian Systems},
volume = {366},
year = {2007},
isbn = {978-3-540-73889-3},
}
@article{NC-MWS:08,
author = {N. Chopra and M. W. Spong},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {353-357},
title = {On exponential synchronization of {Kuramoto}
oscillators},
volume = {54},
year = {2009},
doi = {10.1109/TAC.2008.2007884},
}
@article{JRM-GA-JSS:09,
author = {J. R. Marden and G. Arslan and J. S. Shamma},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {208--220},
title = {Joint strategy fictitious play with inertia for
potential games},
volume = {54},
year = {2009},
doi = {10.1109/TAC.2008.2010885},
}
@article{DB-GN:15,
author = {D. Bauso and G. Notarstefano},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {3107--3112},
title = {Distributed $n$-Player Approachability and Consensus
in Coalitional Games},
volume = {60},
year = {2015},
doi = {10.1109/TAC.2015.2411873},
}
@article{TH-YI-MF-MWS:12,
author = {T. Hatanaka and Y. Igarashi and M. Fujita and
M. W. Spong},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {360--375},
title = {Passivity-based pose synchronization in three
dimensions},
volume = {57},
year = {2012},
doi = {10.1109/TAC.2011.2166668},
}
@article{LS-FF:11,
author = {L. Schenato and F. Fiorentin},
journal = {Automatica},
number = {9},
pages = {1878--1886},
title = {{Average TimeSynch: A} consensus-based protocol for
clock synchronization in wireless sensor networks},
volume = {47},
year = {2011},
doi = {10.1016/j.automatica.2011.06.012},
}
@article{MA:07,
author = {M. Arcak},
journal = {IEEE Transactions on Automatic Control},
number = {8},
pages = {1380-1390},
title = {Passivity as a design tool for group coordination},
volume = {52},
year = {2007},
doi = {10.1109/TAC.2007.902733},
}
@article{JTW-MA:04,
author = {J. T. Wen and M. Arcak},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {162-174},
title = {A unifying passivity framework for network flow
control},
volume = {49},
year = {2004},
doi = {10.1109/TAC.2003.822858},
}
@article{EM-RAF-AKT:16,
author = {E. Mallada and R. A. Freeman and A. K. Tang},
journal = {IEEE Transactions on Control of Network Systems},
number = {1},
pages = {1-12},
title = {Distributed synchronization of heterogeneous
oscillators on networks with arbitrary topology},
volume = {3},
year = {2016},
doi = {10.1109/TCNS.2015.2428371},
}
@book{ANM-RKM:77,
author = {A. N. Michel and R. K. Miller},
publisher = {Academic Press},
title = {Qualitative Analysis of Large Scale Dynamical
Systems},
year = {1977},
isbn = {0-12-493850-7},
}
@book{DDS:78,
author = {D. D. {\v S}iljak},
publisher = {North-Holland},
title = {Large-Scale Dynamic Systems Stability \& Structure},
year = {1978},
isbn = {0486462854},
}
@book{MV:81,
author = {M. Vidyasagar},
publisher = {Springer},
title = {Input-Output Analysis of Large-Scale Interconnected
Systems: {D}ecomposition, Well-Posedness and
Stability},
year = {1981},
isbn = {978-3-540-10501-5},
}
@book{DDS:91,
author = {D. D. {\v S}iljak},
publisher = {Academic Press},
title = {Decentralized Control of Complex Systems},
year = {1991},
isbn = {0-12-643430-1},
}
@book{VL-VMM-SS:91,
author = {V. Lakshmikantham and V. M. Matrosov and
S. Sivasundaram},
publisher = {Kluwer},
title = {Vector {Lyapunov} Functions and Stability Analysis of
Nonlinear Systems},
year = {1991},
isbn = {0792311523},
}
@book{CWW:07,
author = {C. W. Wu},
publisher = {World Scientific Publishing},
title = {Synchronization in Complex Networks of Nonlinear
Dynamical Systems},
year = {2007},
isbn = {978-981-270-973-8},
}
@book{WR-RWB:08,
author = {W. Ren and R. W. Beard},
publisher = {Springer},
series = {Communications and Control Engineering},
title = {Distributed Consensus in Multi-vehicle Cooperative
Control},
year = {2008},
isbn = {978-1-84800-014-8},
}
@book{FB-JC-SM:09,
author = {F. Bullo and J. Cort{\'e}s and S. Mart{\'\i}nez},
publisher = {Princeton University Press},
title = {Distributed Control of Robotic Networks},
year = {2009},
isbn = {978-0-691-14195-4},
url = {https://fbullo.github.io/dcrn},
}
@book{MM-ME:10,
author = {M. Mesbahi and M. Egerstedt},
publisher = {Princeton University Press},
title = {Graph Theoretic Methods in Multiagent Networks},
year = {2010},
isbn = {9781400835355},
}
@book{HB-MA-JW:11,
author = {H. Bai and M. Arcak and J. Wen},
publisher = {Springer},
title = {Cooperative Control Design},
year = {2011},
isbn = {1461429072},
}
@book{EC-BP-AT:14,
author = {E. Cristiani and B. Piccoli and A. Tosin},
publisher = {Springer},
title = {Multiscale Modeling of Pedestrian Dynamics},
year = {2014},
isbn = {978-3-319-06619-6},
}
@book{ZL-ZD:14,
author = {Z. Li and Z. Duan},
publisher = {CRC Press},
title = {Cooperative Control of Multi-Agent Systems: A
Consensus Region Approach},
year = {2014},
isbn = {1466569948},
}
@book{PAF-UH:15,
author = {P. A. Fuhrmann and U. Helmke},
publisher = {Springer},
title = {The Mathematics of Networks of Linear Systems},
year = {2015},
isbn = {3319166468},
}
@book{GC-XW-XL:15,
author = {G. Chen and X. Wang and X. Li},
publisher = {John Wiley \& Sons},
title = {Fundamentals of Complex Networks: Models, Structures
and Dynamics},
year = {2015},
doi = {10.1002/9781118718124},
isbn = {978-1118718117},
}
@book{BAF-MM:16,
author = {B. A. Francis and M. Maggiore},
publisher = {Springer},
title = {Flocking and Rendezvous in Distributed Robotics},
year = {2016},
isbn = {978-3-319-24727-4},
}
@book{MA-CM-AP:16,
author = {M. Arcak and C. Meissen and A. Packard},
publisher = {Springer},
title = {Networks of Dissipative Systems: Compositional
Certification of Stability, Performance, and Safety},
year = {2016},
doi = {10.1007/978-3-319-29928-0},
isbn = {978-3-319-29928-0},
}
@book{MAP-JPG:16,
author = {M. A. Porter and J. P. Gleeson},
publisher = {Springer},
title = {Dynamical Systems on Networks: A Tutorial},
year = {2016},
doi = {10.1007/978-3-319-26641-1},
isbn = {978-3-319-26641-1},
}
@book{FF-PF:17,
author = {F. Fagnani and P. Frasca},
publisher = {Springer},
title = {Introduction to Averaging Dynamics over Networks},
year = {2017},
doi = {10.1007/978-3-319-68022-4},
isbn = {978-3-319-68022-4},
}
@article{SM-JC-FB:04n,
author = {S. Mart{\'\i}nez and J. Cort{\'e}s and F. Bullo},
journal = {{IEEE} Control Systems},
number = {4},
pages = {75-88},
title = {Motion Coordination with Distributed Information},
volume = {27},
year = {2007},
abstract = {This paper surveys recently-developed theoretical
tools for the analysis and design of coordination
algorithms for networks of mobile autonomous agents.
First, various motion coordination tasks are encoded
into aggregate cost functions from Geometric
Optimization. Second, the limited communication
capabilities of the mobile agents are modeled via the
notions of proximity graphs from Computational
Geometry and of spatially distributed maps. Finally,
we illustrate how to apply these tools to design and
analyze scalable cooperative strategies in a variety
of motion coordination problems such as deployment,
rendezvous, and flocking.},
doi = {10.1109/MCS.2007.384124},
}
@article{WR-RWB-EMA:07,
author = {W. Ren and R. W. Beard and E. M. Atkins},
journal = {{IEEE} Control Systems},
number = {2},
pages = {71-82},
title = {Information consensus in multivehicle cooperative
control},
volume = {27},
year = {2007},
doi = {10.1109/MCS.2007.338264},
}
@article{RMM:07,
author = {R. M. Murray},
journal = {ASME Journal of Dynamic Systems, Measurement, and
Control},
number = {5},
pages = {571--583},
title = {Recent research in cooperative control of
multivehicle systems},
volume = {129},
year = {2007},
doi = {10.1115/1.2766721},
}
@article{MEJN:03,
author = {Newman, M. E. J.},
journal = {SIAM Review},
number = {2},
pages = {167--256},
title = {The structure and function of complex networks},
volume = {45},
year = {2003},
doi = {10.1137/S003614450342480},
}
@article{SB-VL-YM-MC-DUH:06,
author = {Boccaletti, S. and Latora, V. and Moreno, Y. and
Chavez, M. and Hwang, D. U.},
journal = {Physics Reports},
number = {4-5},
pages = {175--308},
title = {Complex networks: {S}tructure and dynamics},
volume = {424},
year = {2006},
doi = {10.1016/j.physrep.2005.10.009},
}
@article{CC-SF-VL:09,
author = {Castellano, C. and Fortunato, S. and Loreto, V.},
journal = {Reviews of Modern Physics},
number = {2},
pages = {591--646},
title = {Statistical Physics of Social Dynamics},
volume = {81},
year = {2009},
doi = {10.1103/RevModPhys.81.591},
}
@book{DE-JK:10,
author = {D. Easley and J. Kleinberg},
publisher = {Cambridge University Press},
title = {Networks, Crowds, and Markets: Reasoning About a
Highly Connected World},
year = {2010},
isbn = {0521195330},
}
@book{MOJ:10,
author = {M. O. Jackson},
publisher = {Princeton University Press},
title = {Social and Economic Networks},
year = {2010},
isbn = {0691148201},
}
@book{MEJN:10,
author = {Newman, M. E. J.},
publisher = {Oxford University Press},
title = {Networks: An Introduction},
year = {2010},
isbn = {0199206651},
}
@article{DAS:17,
author = {D. Spielman},
journal = {Bulletin of the American Mathematical Society},
number = {1},
pages = {45--61},
title = {Graphs, Vectors, and Matrices},
volume = {54},
year = {2017},
doi = {10.1090/bull/1557},
}
@incollection{RPA:64,
author = {R. P. Abelson},
booktitle = {Contributions to Mathematical Psychology},
editor = {N. Frederiksen and H. Gulliksen},
pages = {142--160},
publisher = {Holt, Rinehart, \& Winston},
title = {Mathematical models of the distribution of attitudes
under controversy},
volume = {14},
year = {1964},
isbn = {0030430100},
}
@book{NEF-ECJ:11,
author = {N. E. Friedkin and E. C. Johnsen},
publisher = {Cambridge University Press},
title = {Social Influence Network Theory: {A} Sociological
Examination of Small Group Dynamics},
year = {2011},
isbn = {9781107002463},
}
@article{NEF-PJ-FB:14n,
author = {N. E. Friedkin and P. Jia and F. Bullo},
journal = {Sociological Science},
pages = {444-472},
title = {A Theory of the Evolution of Social Power: {N}atural
Trajectories of Interpersonal Influence Systems along
Issue Sequences},
volume = {3},
year = {2016},
abstract = {This article reports new advancements in the theory
of influence system evolution in small deliberative
groups, and a novel set of empirical findings on such
evolution. The theory elaborates the specification of
the single-issue opinion dynamics of such groups,
which has been the focus of theory development in the
field of opinion dynamics, to include group dynamics
that occur along a sequence of issues. The theory
predicts an evolution of influence centralities along
issue sequences based on elementary reflected
appraisal mechanisms that modify influence network
structure and flows of influence in the group. The
new empirical findings, which are also reported in
this article, present a remarkable suite of
issue-sequence effects on influence network structure
consistent with theoretical predictions.},
doi = {10.15195/v3.a20},
}
@article{AGC-HL-JPX:20,
author = {A. G. Chandrasekhar and H. Larreguy and J. P. Xandri},
journal = {Econometrica},
number = {1},
pages = {1-32},
title = {Testing Models of Social Learning on Networks:
Evidence From Two Experiments},
volume = {88},
year = {2020},
abstract = {We theoretically and empirically study an incomplete
information model of social learning. Agents
initially guess the binary state of the world after
observing a private signal. In subsequent rounds,
agents observe their network neighbors' previous
guesses before guessing again. Agents are drawn from
a mixture of learning types—Bayesian, who face
incomplete information about others' types, and
DeGroot, who average their neighbors' previous period
guesses and follow the majority. We study (1)
learning features of both types of agents in our
incomplete information model; (2) what network
structures lead to failures of asymptotic learning;
(3) whether realistic networks exhibit such
structures. We conducted lab experiments with 665
subjects in Indian villages and 350 students from
ITAM in Mexico. We perform a reduced-form analysis
and then structurally estimate the mixing parameter,
finding the share of Bayesian agents to be 10\% and
50\% in the Indian-villager and Mexican-student
samples, respectively.},
doi = {10.3982/ECTA14407},
}
@article{AVP-RT:17,
author = {A. V. Proskurnikov and R. Tempo},
journal = {Annual Reviews in Control},
pages = {65-79},
title = {A Tutorial on Modeling and Analysis of Dynamic Social
Networks. {Part I}},
volume = {43},
year = {2017},
doi = {10.1016/j.arcontrol.2017.03.002},
}
@article{AW-DWK:69,
author = {A. Watton and D. W. Kydon},
journal = {American Journal of Physics},
number = {2},
pages = {220--221},
title = {Analytical Aspects of the {$N$}-Bug Problem},
volume = {37},
year = {1969},
doi = {10.1119/1.1975458},
}
@article{JAM-MEB-BAF:04c,
author = {J. A. Marshall and M. E. Broucke and B. A. Francis},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {1963-1974},
title = {Formations of vehicles in cyclic pursuit},
volume = {49},
year = {2004},
abstract = {Inspired by the so-called "bugs" problem from
mathematics, we study the geometric formations of
multi-vehicle systems under cyclic pursuit. First, we
introduce the notion of cyclic pursuit by examining a
system of identical linear agents in the plane. This
idea is then extended to a system of wheeled
vehicles, each subject to a single nonholonomic
constraint (i.e., unicycles), which is the principal
focus of this article. The pursuit framework is
particularly simple in that the n identical vehicles
are ordered such that vehicle i pursues vehicle i + 1
modulo n. In this article, we assume each vehicle has
the same constant forward speed. We show that the
system's equilibrium formations are generalized
regular polygons and it is exposed how the
multi-vehicle system's global behavior can be shaped
through appropriate controller gain assignments. We
then study the local stability of these equilibrium
polygons, revealing which formations are stable and
which are not. Index Terms: Cooperative control,
multi-agent systems, circulant matrices, pursuit
problems.},
doi = {10.1109/TAC.2004.837589},
}
@article{SLS-MEB-BAF:05,
author = {S. L. Smith and M. E. Broucke and B. A. Francis},
journal = {Automatica},
number = {6},
pages = {1045-1053},
title = {A hierarchical cyclic pursuit scheme for vehicle
networks},
volume = {41},
year = {2005},
doi = {10.1016/j.automatica.2005.01.001},
}
@book{RAH-CRJ:85,
author = {R. A. Horn and C. R. Johnson},
publisher = {Cambridge University Press},
title = {Matrix Analysis},
year = {1985},
isbn = {0521386322},
}
@book{CDM:01,
author = {C. D. Meyer},
publisher = {SIAM},
title = {Matrix Analysis and Applied Linear Algebra},
year = {2001},
annote = {http://www.matrixanalysis.com},
isbn = {0898714540},
}
@book{FRG:59ab,
address = {New York},
author = {Felix R. Gantmacher},
note = {Translation of German edition by K.~A.~Hirsch},
publisher = {Chelsea},
title = {The Theory of Matrices},
volume = {1 and 2},
year = {1959},
isbn = {0-8218-1376-5 and 0-8218-2664-6},
}
@article{OK:1907,
author = {Oskar Perron},
journal = {Mathematische Annalen},
number = {2},
pages = {248--263},
title = {{Zur Theorie der Matrices}},
volume = {64},
year = {1907},
doi = {10.1007/BF01449896},
}
@article{FGF:1912,
author = {Frobenius, Ferdinand Georg},
note = {K{\"o}nigliche Gesellschaft der Wissenschaften},
title = {{\"U}ber Matrizen aus nicht negativen {E}lementen},
year = {1912},
doi = {10.3931/e-rara-18865},
}
@book{LB:92,
author = {L. Breiman},
note = {Corrected reprint of the 1968 original},
publisher = {SIAM},
series = {Classics in Applied Mathematics},
title = {Probability},
volume = {7},
year = {1992},
isbn = {0-89871-296-3},
}
@book{DJH:98,
author = {D. J. Hartfiel},
publisher = {Springer},
title = {Markov Set-Chains},
year = {1998},
doi = {10.1007/BFb0094586},
isbn = {978-3-540-68711-5},
}
@book{LH:13,
edition = {2},
editor = {L. Hogben},
publisher = {Chapman and Hall/CRC},
title = {Handbook of Linear Algebra},
year = {2013},
isbn = {1466507284},
}
@article{JRS:00,
author = {J. R. Silvester},
journal = {The Mathematical Gazette},
number = {501},
pages = {460--467},
title = {Determinants of Block Matrices},
volume = {84},
year = {2000},
doi = {10.2307/3620776},
}
@book{DPB-JNT:97,
author = {D. P. Bertsekas and J. N. Tsitsiklis},
publisher = {Athena Scientific},
title = {Parallel and Distributed Computation: Numerical
Methods},
year = {1997},
annote = {This book is a comprehensive and theoretically sound
treatment of parallel and distributed numerical
methods. It focuses on algorithms that are naturally
suited for massive parallelization, and it explores
the fundamental convergence, rate of convergence,
communication, and synchronization issues associated
with such algorithms.},
isbn = {1886529019},
}
@article{TAM-YU:11,
author = {T. A. Davis and Y. Hu},
journal = {ACM Transactions on Mathematical Software},
number = {1},
pages = {1-25},
title = {The {University of Florida} sparse matrix collection},
volume = {38},
year = {2011},
abstract = {We describe the University of Florida Sparse Matrix
Collection, a large and actively growing set of
sparse matrices that arise in real applications. The
Collection is widely used by the numerical linear
algebra community for the development and performance
evaluation of sparse matrix algorithms. It allows for
robust and repeatable experiments: robust because
performance results with artificially-generated
matrices can be misleading, and repeatable because
matrices are curated and made publicly available in
many formats. Its matrices cover a wide spectrum of
domains, include those arising from problems with
underlying 2D or 3D geometry (as structural
engineering, computational fluid dynamics, model
reduction, electromagnetics, semiconductor devices,
thermodynamics, materials, acoustics, computer
graphics/vision, robotics/kinematics, and other
discretizations) and those that typically do not have
such geometry (optimization, circuit simulation,
economic and financial modeling, theoretical and
quantum chemistry, chemical process simulation,
mathematics and statistics, power networks, and other
networks and graphs). We provide software for
accessing and managing the Collection, from MATLAB,
Mathematica, Fortran, and C, as well as an online
search capability. Graph visualization of the
matrices is provided, and a new multilevel coarsening
scheme is proposed to facilitate this task.},
doi = {10.1145/2049662.2049663},
}
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Information and Computer Sciences},
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year = {2008},
url = {http://networkdata.ics.uci.edu},
}
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D. A. Pierre},
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note = {Also in Opera Omnia (1), Vol. 7, 1-10.},
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title = {{Solutio Problematis ad Geometriam Situs
Pertinentis}},
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man bei der Untersuchung der linearen Verteilung
galvanischer Str\"ome gef\"uhrt wird}},
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edition = {2},
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volume = {173},
year = {2000},
annote = {Reference for Metric Graphs},
isbn = {3642142788},
}
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title = {Modern Graph Theory},
year = {1998},
isbn = {0387984887},
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number = {1},
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year = {1962},
doi = {10.1007/BF01386304},
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year = {2005},
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@book{LL:19,
author = {Lov{\'a}sz, L{\'a}szl{\'o}},
publisher = {American Mathematical Society},
title = {Graphs and Geometry},
year = {2019},
isbn = {9781470450878},
}
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publisher = {Springer},
title = {Algebraic Graph Theory},
year = {2001},
isbn = {0387952411},
}
@misc{MI:16,
author = {M. Idel},
note = {arXiv preprint arXiv:1609.06349},
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form for matrices and positive maps},
year = {2016},
}
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year = {1981},
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year = {2002},
doi = {10.1017/S0963548301004928},
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volume = {281},
year = {2004},
doi = {10.1016/j.disc.2003.08.005},
}
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@incollection{BCE-AJH-UGR-HS:85,
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H. Schneider},
booktitle = {Mathematical Programming Essays in Honor of George B.
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publisher = {Springer},
title = {Line-sum-symmetric scalings of square nonnegative
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}
@inproceedings{MBC-AM-DT-AV:17,
author = {M. B. Cohen and A. Madry and D. Tsipras and A. Vladu},
booktitle = {2017 {IEEE} 58th Annual Symposium on Foundations of
Computer Science ({FOCS})},
month = oct,
title = {Matrix Scaling and Balancing via Box Constrained
Newton{\textquotesingle}s Method and Interior Point
Methods},
year = {2017},
doi = {10.1109/focs.2017.88},
}
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author = {P. J. Davis},
publisher = {John Wiley \& Sons},
title = {Circulant Matrices},
year = {1979},
isbn = {0-471-05771-1},
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title = {Product of Indecomposable, Aperiodic, Stochastic
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volume = {14},
year = {1963},
doi = {10.1090/S0002-9939-1963-0154756-3},
}
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title = {{Unzerlegbare, nicht negative Matrizen}},
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year = {1950},
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title = {Combinatorial Matrix Theory},
year = {1991},
isbn = {0521322650},
}
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author = {P. H. Leslie},
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author = {H. Caswell},
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publisher = {Sinauer Associates},
title = {Matrix Population Models},
year = {2006},
isbn = {087893121X},
}
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author = {D. Krackhardt},
journal = {Social Networks},
number = {2},
pages = {109-134},
title = {Cognitive social structures},
volume = {9},
year = {1987},
doi = {10.1016/0378-8733(87)90009-8},
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author = {DeMarzo, P. M. and Vayanos, D. and Zwiebel, J.},
journal = {Quarterly Journal of Economics},
number = {3},
pages = {909-968},
title = {Persuasion Bias, Social Influence, and Unidimensional
Opinions},
volume = {118},
year = {2003},
doi = {10.1162 /00335530360698469},
}
@article{PB:72c,
author = {P. Bonacich},
journal = {Journal of Mathematical Sociology},
number = {1},
pages = {113--120},
title = {Factoring and weighting approaches to status scores
and clique identification},
volume = {2},
year = {1972},
doi = {10.1080/0022250X.1972.9989806},
}
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author = {L. Katz},
journal = {Psychometrika},
number = {1},
pages = {39--43},
title = {A new status index derived from sociometric analysis},
volume = {18},
year = {1953},
doi = {10.1007/BF02289026},
}
@article{HI-RT:14,
author = {H. Ishii and R. Tempo},
journal = {{IEEE} Control Systems},
number = {3},
pages = {34--53},
title = {The {PageRank} Problem, Multiagent Consensus, and Web
Aggregation: {A} Systems and Control Viewpoint},
volume = {34},
year = {2014},
doi = {10.1109/MCS.2014.2308672},
}
@article{DFG:14,
author = {D. F. Gleich},
journal = {SIAM Review},
number = {3},
pages = {321-363},
title = {{PageRank} beyond the {W}eb},
volume = {57},
year = {2015},
doi = {10.1137/140976649},
}
@article{SPB-MGE:06,
author = {S. P. Borgatti and M. G. Everett},
journal = {Social Networks},
number = {4},
pages = {466--484},
title = {A graph-theoretic perspective on centrality},
volume = {28},
year = {2006},
doi = {10.1016/j.socnet.2005.11.005},
}
@misc{UB:06,
address = {Bloomington, IN, USA},
author = {U. Brandes},
howpublished = {Slides},
month = may,
note = {The International Workshop/School and Conference on
Network Science},
title = {Centrality: concepts and methods},
year = {2006},
url = {http://vw.indiana.edu/netsci06},
}
@article{AAM:1906,
author = {Andrey A. Markov},
journal = {Izvestiya Fiziko-matematicheskogo obschestva pri
Kazanskom universitete},
note = {(in Russian)},
title = {Extensions of the law of large numbers to dependent
quantities},
volume = {15},
year = {1906},
}
@article{RLD:1956,
author = {Dobrushin, R. L.},
journal = {Theory of Probability \& Its Applications},
number = {1},
pages = {65-80},
title = {Central Limit Theorem for Nonstationary {Markov}
Chains. {I}},
volume = {1},
year = {1956},
doi = {10.1137/1101006},
}
@article{ES:73,
author = {Seneta, E.},
journal = {Mathematical Proceedings of the Cambridge
Philosophical Society},
number = {3},
pages = {507--513},
title = {On the historical development of the theory of finite
inhomogeneous {Markov} chains},
volume = {74},
year = {1973},
doi = {10.1017/S0305004100077276},
}
@article{ICFI-TMS:11,
author = {I. C. F. Ipsen and T. M. Selee},
journal = {SIAM Journal on Matrix Analysis and Applications},
number = {1},
pages = {153-200},
title = {Ergodicity Coefficients Defined by Vector Norms},
volume = {32},
year = {2011},
doi = {10.1137/090752948},
}
@article{JL-SM-ASM-BDOA-CY:11,
author = {J. Liu and S. Mou and A. S. Morse and
B. D. O. Anderson and C. Yu},
journal = {Proceedings of the IEEE},
number = {9},
pages = {1505-1524},
title = {Deterministic Gossiping},
volume = {99},
year = {2011},
abstract = {For the purposes of this paper, “gossiping” is a
distributed process whose purpose is to enable the
members of a group of autonomous agents to
asymptotically determine, in a decentralized manner,
the average of the initial values of their scalar
gossip variables. This paper discusses several
different deterministic protocols for gossiping which
avoid deadlocks and achieve consensus under different
assumptions. First considered is $T$-periodic gossiping
which is a gossiping protocol which stipulates that
each agent must gossip with the same neighbor exactly
once every $T$ time units. Among
the results discussed is the fact that if the
underlying graph characterizing neighbor relations is
a tree, convergence is exponential at a worst case
rate which is the same for all possible $T$ -periodic gossip
sequences associated with the graph. Many gossiping
protocols are request based which means simply that a
gossip between two agents will occur whenever one of
the two agents accepts a request to gossip placed by
the other. Three deterministic request-based
protocols are discussed. Each is guaranteed to not
deadlock and to always generate sequences of gossip
vectors which converge exponentially fast. It is
shown that worst case convergence rates can be
characterized in terms of the second largest singular
values of suitably defined doubly stochastic
matrices.},
doi = {10.1109/JPROC.2011.2159689},
}
@article{RM-FJH:20,
author = {R. Marsli and F. J. Hall},
journal = {Linear and Multilinear Algebra},
number = {10},
pages = {1886--1906},
title = {Some properties of ergodicity coefficients with
applications in spectral graph theory},
volume = {70},
year = {2020},
abstract = {The main result is Corollary 2.9 which provides upper
bounds on, and even better, approximates the largest
non-trivial eigenvalue in absolute value of real
constant row-sum matrices by the use of vector
norm-based ergodicity coefficients {τp}. If the
constant row-sum matrix is nonsingular, then it is
also shown how its smallest non-trivial eigenvalue in
absolute value can be bounded by using {τp}. In the
last section, these two results are applied to bound
the spectral radius of the Laplacian matrix as well
as the algebraic connectivity of its associated
graph. Many other results are obtained. In
particular, Theorem 2.15 is a convergence theorem
for τp and Theorem 4.7 says that τ1 is less than
or equal to τ∞ for the Laplacian matrix of every
simple graph. An application related to the stability
of Markov chains is discussed. Other discussions,
open questions and examples are provided.},
doi = {10.1080/03081087.2020.1777251},
}
@article{RH-UK:02,
author = {R. Hegselmann and U. Krause},
journal = {Journal of Artificial Societies and Social
Simulation},
number = {3},
title = {Opinion dynamics and bounded confidence models,
analysis, and simulations},
volume = {5},
year = {2002},
url = {http://jasss.soc.surrey.ac.uk/5/3/2.html},
}
@article{AM-FB:11f,
author = {A. MirTabatabaei and F. Bullo},
journal = {SIAM Journal on Control and Optimization},
number = {5},
pages = {2763-2785},
title = {Opinion Dynamics in Heterogeneous Networks:
{C}onvergence Conjectures and Theorems},
volume = {50},
year = {2012},
abstract = {Recently, significant attention has been dedicated to
the models of opinion dynamics in which opinions are
described by real numbers, and agents update their
opinions synchronously by averaging their neighbors'
opinions. The neighbors of each agent can be defined
as either (1) those agents whose opinions are in its
``confidence range,'' or (2) those agents whose
``influence range'' contain the agent's opinion. The
former definition is employed in Hegselmann and
Krause's bounded confidence model, and the latter is
novel here. As the confidence and influence ranges
are distinct for each agent, the heterogeneous
state-dependent interconnection topology leads to a
poorly-understood complex dynamic behavior. In both
models, we classify the agents via their
interconnection topology and, accordingly, compute
the equilibria of the system. Then, we define a
positive invariant set centered at each equilibrium
opinion vector. We show that if a trajectory enters
one such set, then it converges to a steady state
with constant interconnection topology. This result
gives us a novel sufficient condition for both models
to establish convergence, and is consistent with our
conjecture that all trajectories of the bounded
confidence and influence models eventually converge
to a steady state under fixed topology. Furthermore,
we study the trajectories of systems with fixed
interconnection topology, and prove the existence of
a leader group for each group of agents that
determines the follower's rate and direction of
convergence.},
doi = {10.1137/11082751X},
}
@book{UB-TE:05,
author = {U. Brandes and T. Erlebach},
journal = {Lecture Notes in Computer Science},
publisher = {Springer},
title = {Network Analysis: Methodological Foundations},
year = {2005},
isbn = {3540249796},
}
@article{AB:50,
author = {A. Bavelas},
journal = {Journal of the Acoustical Society of America},
pages = {725-730},
title = {Communication patterns in task-oriented groups},
volume = {22},
year = {1950},
doi = {10.1121/1.1906679},
}
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author = {L. C. Freeman},
journal = {Sociometry},
number = {1},
pages = {35-41},
title = {A set of measures of centrality based on betweenness},
volume = {40},
year = {1977},
doi = {10.2307/3033543},
}
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author = {P. Bonacich},
journal = {Sociological Methodology},
pages = {176--185},
title = {Technique for analyzing overlapping memberships},
volume = {4},
year = {1972},
doi = {10.2307/270732},
}
@article{JMK:99,
author = {J. M. Kleinberg},
journal = {Journal of the ACM},
number = {5},
pages = {604--632},
title = {Authoritative Sources in a Hyperlinked Environment},
volume = {46},
year = {1999},
doi = {10.1145/324133.324140},
}
@article{SB-LP:98,
author = {S. Brin and L. Page},
journal = {Computer Networks},
pages = {107-117},
title = {The anatomy of a large-scale hypertextual {W}eb
search engine},
volume = {30},
year = {1998},
doi = {10.1016/S0169-7552(98)00110-X},
}
@misc{LP:01,
author = {L. Page},
month = sep,
note = {US Patent 6,285,999},
publisher = {Google Patents},
title = {Method for node ranking in a linked database},
year = {2001},
url = {https://www.google.com/patents/US6285999},
}
@article{NEF:91,
author = {N. E. Friedkin},
journal = {Social Problems},
number = {6},
pages = {1478-1504},
title = {Theoretical foundations for centrality measures},
volume = {96},
year = {1991},
doi = {10.1086/229694},
}
@article{NEF-ECJ:14,
author = {N. E. Friedkin and E. C. Johnsen},
journal = {Social Networks},
pages = {12--13},
title = {Two steps to obfuscation},
volume = {39},
year = {2014},
doi = {10.1016/j.socnet.2014.03.008},
}
@article{YN:12,
author = {Y. Nesterov},
journal = {SIAM Journal on Optimization},
number = {2},
pages = {341-362},
title = {Efficiency of coordinate descent methods on
huge-scale optimization problems},
volume = {22},
year = {2012},
doi = {10.1137/100802001},
}
@article{HI-RT:10,
author = {H. Ishii and R. Tempo},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {1987-2002},
title = {Distributed Randomized Algorithms for the {PageRank}
Computation},
volume = {55},
year = {2010},
doi = {10.1109/TAC.2010.2042984},
}
@article{WXZ-HFC-HTF:13,
author = {W. X. Zhao and H. F. Chen and H. T. Fang},
journal = {IEEE Transactions on Automatic Control},
number = {12},
pages = {3255-3259},
title = {Convergence of distributed randomized {PageRank}
algorithms},
volume = {58},
year = {2013},
doi = {10.1109/TAC.2013.2264553},
}
@article{MG-SJ-FB:17b,
author = {M. George and S. Jafarpour and F. Bullo},
journal = {IEEE Transactions on Automatic Control},
number = {4},
pages = {1566-1580},
title = {Markov Chains with Maximum Entropy for Robotic
Surveillance},
volume = {64},
year = {2019},
abstract = {This article provides a comprehensive analysis of the
following optimization problem: maximize the entropy
rate generated by a Markov chain over a connected
graph of order~$n$ and subject to a prescribed
stationary distribution. First, we show that this
problem is strictly convex with global optimum lying
in the interior of the feasible space. Second, using
Lagrange multipliers we provide a closed-form
expression for the maxentropic Markov chain as a
function of an $n$-dimensional vector, referred to as
the maxentropic vector; we provide a
provably-converging iteration to compute this vector.
Third, we show that the maxentropic Markov chain is
reversible, compute its entropy rate, and describe
special cases, among other results. Fourth, through
analysis and simulations, we show that our proposed
procedure is more computationally efficient than
semidefinite programming methods. Finally, we apply
these results to robotic surveillance problems. We
show realizations of the maxentropic Markov chains
over prototypical robotic roadmaps and find that
maxentropic Markov chains outperform minimum mean
hitting time Markov chains for so-called
``intelligent intruders'' with short attack
durations.},
doi = {10.1109/TAC.2018.2844120},
}
@inproceedings{DK-AD-JG:03,
address = {Washington, DC},
author = {D. Kempe and A. Dobra and J. Gehrke},
booktitle = {IEEE Symposium on Foundations of Computer Science},
month = oct,
pages = {482-491},
title = {Gossip-Based Computation of Aggregate Information},
year = {2003},
doi = {10.1109/SFCS.2003.1238221},
}
@article{AO-JNT:07,
author = {A. Olshevsky and J. N. Tsitsiklis},
journal = {SIAM Journal on Control and Optimization},
number = {1},
pages = {33-55},
title = {Convergence Speed in Distributed Consensus and
Averaging},
volume = {48},
year = {2009},
annote = {We study the convergence speed of distributed
iterative algorithms for the consensus and averaging
problems, with emphasis on the latter. We first
consider the case of a fixed communication topology.
We show that a simple adaptation of a consensus
algorithm leads to an averaging algorithm. We prove
lower bounds on the worst-case convergence time for
various classes of linear, time-invariant,
distributed consensus methods, and provide an
algorithm that essentially matches those lower
bounds. We then consider the case of a time-varying
topology, and provide a polynomial-time averaging
algorithm.},
doi = {10.1137/060678324},
}
@inproceedings{FB-VB-PT-JT-MV:10,
author = {F. Benezit and V. Blondel and P. Thiran and
J. Tsitsiklis and M. Vetterli},
booktitle = {IEEE International Symposium on Information Theory},
month = jun,
pages = {1753-1757},
title = {Weighted gossip: {D}istributed averaging using
non-doubly stochastic matrices},
year = {2010},
doi = {10.1109/ISIT.2010.5513273},
}
@article{ZB-JD-JML-BW:09,
author = {Z. Burda and J. Duda and J. M. Luck and B. Waclaw},
journal = {Physical Review Letters},
pages = {160602},
title = {Localization of the Maximal Entropy Random Walk},
volume = {102},
year = {2009},
doi = {10.1103/PhysRevLett.102.160602},
}
@article{NM-AWR-MNR-AHT-ET:53,
author = {N. Metropolis and A. W. Rosenbluth and
M. N. Rosenbluth and A. H. Teller and E. Teller},
journal = {Journal of Chemical Physics},
number = {6},
pages = {1087--1092},
title = {Equation of State Calculations by Fast Computing
Machines},
volume = {21},
year = {1953},
doi = {10.1063/1.1699114},
}
@incollection{LL:93,
author = {L. Lov{\'a}sz},
booktitle = {{Combinatorics: Paul Erd\H{o}s is Eighty}},
editor = {D. Mikl\'os, V. T. S\'os, T. Sz\"onyi},
pages = {353-398},
publisher = {J\'anos Bolyai Mathematical Society},
title = {Random Walks on Graphs: {A} Survey},
volume = {2},
year = {1993},
isbn = {9638022744},
}
@article{ES:88,
author = {Seneta, E.},
journal = {Advances in Applied Probability},
number = {1},
pages = {228-230},
title = {Perturbation of the stationary distribution measured
by ergodicity coefficients},
volume = {20},
year = {1988},
doi = {10.2307/1427277},
}
@article{GEC-CDM:01,
author = {G. E. Cho and C. D. Meyer},
journal = {Linear Algebra and its Applications},
number = {1},
pages = {137-150},
title = {Comparison of perturbation bounds for the stationary
distribution of a {M}arkov chain},
volume = {335},
year = {2001},
doi = {10.1016/S0024-3795(01)00320-2},
}
@incollection{NEF-ECJ:99,
author = {N. E. Friedkin and E. C. Johnsen},
booktitle = {Advances in Group Processes},
editor = {S. R. Thye and E. J. Lawler and M. W. Macy and
H. A. Walker},
pages = {1-29},
publisher = {Emerald Group Publishing Limited},
title = {Social influence networks and opinion change},
volume = {16},
year = {1999},
isbn = {0762304529},
}
@article{DB-JK-SO:15,
author = {D. Bindel and J. Kleinberg and S. Oren},
journal = {Games and Economic Behavior},
pages = {248-265},
title = {How bad is forming your own opinion?},
volume = {92},
year = {2015},
abstract = {Abstract: The question of how people form their
opinion has fascinated economists and sociologists
for long time. In many of the models, a group of
people in a social network, each holding a numerical
opinion, arrive at a shared opinion through repeated
averaging with their neighbors in the network.
Motivated by the observation that in reality
consensus is rarely reached, we study a related
sociological model in which individuals' intrinsic
beliefs counterbalance the averaging process and
yield a diversity of opinions. We interpret the
repeated averaging process as best-response dynamics
in an underlying game with natural payoffs and its
limit as an equilibrium. This allows us to study the
cost of disagreement by comparing between the cost at
equilibrium and the social optimum. We also consider
a natural network design problem in this setting:
which links can we add to the underlying network to
reduce the cost at equilibrium?},
doi = {10.1016/j.geb.2014.06.004},
}
@article{CR-PF-RT-HI:15,
author = {C. Ravazzi and P. Frasca and R. Tempo and H. Ishii},
journal = {IEEE Transactions on Control of Network Systems},
number = {1},
pages = {78-87},
title = {Ergodic randomized algorithms and dynamics over
networks},
volume = {2},
year = {2015},
doi = {10.1109/TCNS.2014.2367571},
}
@article{WKH:70,
author = {W. K. Hastings},
journal = {Biometrika},
number = {1},
pages = {97--109},
title = {Monte {C}arlo sampling methods using {M}arkov chains
and their applications},
volume = {57},
year = {1970},
abstract = {{A generalization of the sampling method introduced
by Metropolis et al. (1953) is presented along with
an exposition of the relevant theory, techniques of
application and methods and difficulties of assessing
the error in Monte Carlo estimates. Examples of the
methods, including the generation of random
orthogonal matrices and potential applications of the
methods to numerical problems arising in statistics,
are discussed.}},
doi = {10.1093/biomet/57.1.97},
}
@article{LJB-PD:01,
author = {L. J. Billera and P. Diaconis},
journal = {Statistical Science},
number = {4},
pages = {335--339},
title = {A Geometric Interpretation of the
{M}etropolis-{H}astings Algorithm},
volume = {16},
year = {2001},
abstract = {The Metropolis-Hastings algorithm transforms a given
stochastic matrix into a reversible stochastic matrix
with a prescribed stationary distribution. We show
that this transformation gives the minimum distance
solution in an $L^1$ metric.},
doi = {10.1214/ss/1015346318},
}
@article{JB:16,
author = {J. Bierkens},
journal = {Statistics and Computing},
number = {6},
pages = {1213-1228},
title = {Non-reversible {Metropolis}-{Hastings}},
volume = {26},
year = {2016},
abstract = {The classical Metropolis-Hastings (MH) algorithm can
be extended to generate non-reversible Markov chains.
This is achieved by means of a modification of the
acceptance probability, using the notion of vorticity
matrix. The resulting Markov chain is non-reversible.
Results from the literature on asymptotic variance,
large deviations theory and mixing time are
mentioned, and in the case of a large deviations
result, adapted, to explain how non-reversible Markov
chains have favorable properties in these respects.
We provide an application of NRMH in a continuous
setting by developing the necessary theory and
applying, as first examples, the theory to Gaussian
distributions in three and nine dimensions. The
empirical autocorrelation and estimated asymptotic
variance for NRMH applied to these examples show
significant improvement compared to MH with identical
stepsize.},
doi = {10.1007/s11222-015-9598-x},
}
@article{MF:73,
author = {M. Fiedler},
journal = {Czechoslovak Mathematical Journal},
number = {2},
pages = {298--305},
publisher = {Institute of Mathematics, Academy of Sciences of the
Czech Republic},
title = {Algebraic connectivity of graphs},
volume = {23},
year = {1973},
url = {http://dml.cz/dmlcz/101168},
}
@article{DJK-MR:93,
author = {D. J. Klein and M. Randi{\'c}},
journal = {Journal of Mathematical Chemistry},
number = {1},
pages = {81--95},
title = {Resistance distance},
volume = {12},
year = {1993},
doi = {10.1007/BF01164627},
}
@misc{DG:06,
author = {D. Gleich},
institution = {Purdue University},
month = jan,
note = {(Last retrieved on Dec 1, 2021)},
title = {{Spectral Graph Partitioning and the Laplacian with
Matlab}},
year = {2006},
url = {https://www.cs.purdue.edu/homes/dgleich/demos/matlab/
spectral/spectral.html},
}
@incollection{BM:91,
author = {B. Mohar},
booktitle = {Graph Theory, Combinatorics, and Applications},
editor = {Y. Alavi and G. Chartrand and O. R. Oellermann and
A. J. Schwenk},
pages = {871-898},
publisher = {John Wiley \& Sons},
title = {The {L}aplacian spectrum of graphs},
volume = {2},
year = {1991},
isbn = {0471532452},
url = {http://citeseerx.ist.psu.edu/viewdoc/summary?
doi=10.1.1.96.2577},
}
@article{RM:94,
author = {R. Merris},
journal = {Linear Algebra and its Applications},
pages = {143-176},
title = {Laplacian matrices of a graph: {A} survey},
volume = {197},
year = {1994},
doi = {10.1016/j.laa.2011.11.032 3374},
}
@article{NMMdA:07,
author = {N. M. {Maia~de~Abreu}},
journal = {Linear Algebra and its Applications},
number = {1},
pages = {53-73},
title = {Old and new results on algebraic connectivity of
graphs},
volume = {423},
year = {2007},
doi = {10.1016/j.laa.2006.08.017},
}
@article{NKV:13,
author = {N. K. Vishnoi},
journal = {Theoretical Computer Science},
number = {1-2},
pages = {1--141},
title = {${Lx=b}$, {L}aplacian Solvers and Their Algorithmic
Applications},
volume = {8},
year = {2013},
doi = {10.1561/0400000054},
}
@article{DF:72,
author = {D. Fife},
journal = {Mathematical Biosciences},
number = {3},
pages = {311--315},
title = {Which linear compartmental systems contain traps?},
volume = {14},
year = {1972},
doi = {10.1016/0025-5564(72)90082-X},
}
@article{DMF-JAJ:75,
author = {D. M. Foster and J. A. Jacquez},
journal = {Mathematical Biosciences},
number = {1},
pages = {89--97},
title = {Multiple zeros for eigenvalues and the multiplicity
of traps of a linear compartmental system},
volume = {26},
year = {1975},
doi = {10.1016/0025-5564(75)90096-6},
}
@article{RPA-PYC:00,
author = {R. P. Agaev and P. Y. Chebotarev},
journal = {Automation and Remote Control},
number = {9},
pages = {1424-1450},
title = {The matrix of maximum out forests of a digraph and
its applications},
volume = {61},
year = {2000},
abstract = {We study the maximum out forests of a (weighted)
digraph and the matrix of maximum out forests. A
maximum out forest of a digraph Gamma is a spanning
subgraph of Gamma that consists of disjoint diverging
trees and has the maximum possible number of arcs. If
a digraph contains out arborescences, then maximum
out forests coincide with them. We consider Markov
chains related to a weighted digraph and prove that
the matrix of Cesaro limiting probabilities of such a
chain coincides with the normalized matrix of maximum
out forests. This provides an interpretation for the
matrix of Cesasro limiting probabilities of an
arbitrary stationary finite Markov chain in terms of
the weight of maximum out forests. We discuss the
applications of the matrix of maximum out forests and
its transposition, the matrix of limiting
accessibilities of a digraph, to the problems of
preference aggregation, measuring the vertex
proximity, and uncovering the structure of a
digraph.},
url = {https://arxiv.org/pdf/math/0602059},
}
@article{ZL-BF-MM:05,
author = {Z. Lin and B. Francis and M. Maggiore},
journal = {IEEE Transactions on Automatic Control},
number = {1},
pages = {121-127},
title = {Necessary and sufficient graphical conditions for
formation control of unicycles},
volume = {50},
year = {2005},
doi = {10.1109/TAC.2004.841121},
}
@article{WR-RWB:05,
author = {W. Ren and R. W. Beard},
journal = {IEEE Transactions on Automatic Control},
number = {5},
pages = {655-661},
title = {Consensus seeking in multiagent systems under
dynamically changing interaction topologies},
volume = {50},
year = {2005},
abstract = {This note considers the problem of information
consensus among multiple agents in the presence of
limited and unreliable information exchange with
dynamically changing interaction topologies. Both
discrete and continuous update schemes are proposed
for information consensus. This note shows that
information consensus under dynamically changing
interaction topologies can be achieved asymptotically
if the union of the directed interaction graphs have
a spanning tree frequently enough as the system
evolves.},
doi = {10.1109/TAC.2005.846556},
}
@article{IG-WX:04,
author = {I. Gutman and W. Xiao},
journal = {Bulletin (Académie Serbe des Sciences et des Arts.
Classe des sciences mathématiques et naturelles.
Sciences mathématiques)},
number = {29},
pages = {15--23},
title = {Generalized inverse of the {L}aplacian matrix and
some applications},
volume = {129},
year = {2004},
url = {http://emis.ams.org/journals/BSANU/29/2.html},
}
@article{FD-JWSP-FB:17k,
author = {F. D{\"o}rfler and J. W. Simpson-Porco and F. Bullo},
journal = {Proceedings of the IEEE},
number = {5},
pages = {977-1005},
title = {Electrical Networks and Algebraic Graph Theory:
{M}odels, Properties, and Applications},
volume = {106},
year = {2018},
abstract = {Algebraic graph theory is a cornerstone in the study
of electrical networks ranging from miniature
integrated circuits to continental-scale power
systems. Conversely, many fundamental results of
algebraic graph theory were laid out by early
electrical circuit analysts. In this paper we survey
some fundamental and historic as well as recent
results on how algebraic graph theory informs
electrical network analysis, dynamics, and design. In
particular, we review the algebraic and spectral
properties of graph adjacency, Laplacian, incidence,
and resistance matrices and how they relate to the
analysis, network-reduction, and dynamics of certain
classes of electrical networks. We study these
relations for models of increasing complexity ranging
from static resistive DC circuits, over dynamic RLC
circuits, to nonlinear AC power flow. We conclude
this paper by presenting a set of fundamental open
questions at the intersection of algebraic graph
theory and electrical networks.},
doi = {10.1109/JPROC.2018.2821924},
}
@article{MAP-JPO-PJM:09,
author = {M. A. Porter and J.-P. Onnela and P. J. Mucha},
journal = {Notices of the AMS},
number = {9},
pages = {1082--1097},
title = {Communities in networks},
volume = {56},
year = {2009},
url = {http://www.ams.org/notices/200909/rtx090901082p.pdf},
}
@article{SF:10,
author = {S. Fortunato},
journal = {Physics Reports},
number = {3-5},
pages = {75--174},
title = {Community detection in graphs},
volume = {486},
year = {2010},
doi = {10.1016/j.physrep.2009.11.002},
}
@inproceedings{RC-AC-LS-SZ:08,
author = {R. Carli and A. Chiuso and L. Schenato and
S. Zampieri},
booktitle = {{IFAC} {W}orld {C}ongress},
pages = {10289-10294},
title = {A {PI} Consensus Controller for Networked Clocks
Synchronization},
volume = {41},
year = {2008},
doi = {10.3182/20080706-5-KR-1001.01741},
}
@article{RC-SZ:14,
author = {R. Carli and S. Zampieri},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {409-422},
title = {Network Clock Synchronization Based on the
Second-Order Linear Consensus Algorithm},
volume = {59},
year = {2014},
doi = {10.1109/TAC.2013.2283742},
}
@article{EM-XM-MH-LZ-AT:15,
author = {E. Mallada and X. Meng and M. Hack and L. Zhang and
A. Tang},
journal = {IEEE/ACM Transactions on Networking},
number = {5},
pages = {1619--1633},
title = {Skewless network clock synchronization without
discontinuity: {C}onvergence and performance},
volume = {23},
year = {2015},
doi = {10.1109/TNET.2014.2345692},
}
@article{BS-UB-ADK:05,
author = {B. Sundararaman and U. Buy and A. D. Kshemkalyani},
journal = {Ad Hoc Networks},
number = {3},
pages = {281-323},
title = {Clock synchronization for wireless sensor networks: a
survey},
volume = {3},
year = {2005},
doi = {10.1016/j.adhoc.2005.01.002},
}
@article{FS-BY:04,
author = {F. Sivrikaya and B. Yener},
journal = {IEEE Network},
number = {4},
pages = {45--50},
title = {Time synchronization in sensor networks: {A} survey},
volume = {18},
year = {2004},
doi = {10.1109/MNET.2004.1316761},
}
@article{OS-US-YBN-SS:08,
author = {Simeone, O. and Spagnolini, U. and Bar-Ness, Y. and
Strogatz, S. H.},
journal = {IEEE Signal Processing Magazine},
number = {5},
pages = {81--97},
title = {Distributed synchronization in wireless networks},
volume = {25},
year = {2008},
doi = {10.1109/MSP.2008.926661},
}
@article{NR:12,
author = {N. Reff},
journal = {Linear Algebra and its Applications},
number = {9},
pages = {3165--3176},
title = {Spectral properties of complex unit gain graphs},
volume = {436},
year = {2012},
doi = {10.1016/j.laa.2011.10.021},
}
@article{ZL-WD-GY-CY-AG:13,
author = {Z. Lin and W. Ding and G. Yan and C. Yu and A. Giua},
journal = {Automatica},
number = {6},
pages = {1900--1906},
title = {Leader--follower formation via complex {L}aplacian},
volume = {49},
year = {2013},
doi = {10.1016/j.automatica.2013.02.055},
}
@misc{JGD-LQ:14,
author = {J.-G. Dong and L. Qiu},
title = {Complex {L}aplacians and Applications in Multi-Agent
Systems},
year = {2014},
url = {https://arxiv.org/pdf/1406.1862},
}
@article{CG-JC-FB:06o,
author = {C. Gao and J. Cort{\'e}s and F. Bullo},
journal = {Automatica},
number = {8},
pages = {2120-2127},
title = {Notes on Averaging over Acyclic Digraphs and Discrete
Coverage Control},
volume = {44},
year = {2008},
abstract = {In this paper, we show the relationship between two
algorithms and optimization problems that are the
subject of recent attention in the networking and
control literature. First, we obtain some results on
averaging algorithms over acyclic digraphs with fixed
and controlled-switching topology. Second, we discuss
continuous and discrete coverage control laws.
Further, we show how discrete coverage control laws
can be cast as averaging algorithms defined over
discrete Voronoi graphs.},
doi = {10.1016/j.automatica.2007.12.017},
}
@article{FD-FB:11d,
author = {F. D{\"o}rfler and F. Bullo},
journal = {IEEE Transactions on Circuits and Systems~I: Regular
Papers},
number = {1},
pages = {150-163},
title = {Kron Reduction of Graphs with Applications to
Electrical Networks},
volume = {60},
year = {2013},
abstract = {Consider a weighted and undirected graph, possibly
with self-loops, and its corresponding Laplacian
matrix, possibly augmented with additional diagonal
elements corresponding to the self-loops. The Kron
reduction of this graph is again a graph whose
Laplacian matrix is obtained by the Schur complement
of the original Laplacian matrix with respect to a
subset of nodes. The Kron reduction process is
ubiquitous in classic circuit theory and in related
disciplines such as electrical impedance tomography,
smart grid monitoring, transient stability assessment
in power networks, or analysis and simulation of
induction motors and power electronics. More general
applications of Kron reduction occur in sparse matrix
algorithms, multi-grid solvers, finite-element
analysis, and Markov chains. The Schur complement of
a Laplacian matrix and related concepts have also
been studied under different names and as purely
theoretic problems in the literature on linear
algebra. In this paper we propose a general
graph-theoretic framework for Kron reduction that
leads to novel and deep insights both on the
mathematical and the physical side. We show the
applicability of our framework to various practical
problem setups arising in engineering applications
and computation. Furthermore, we provide a
comprehensive and detailed graph-theoretic analysis
of the Kron reduction process encompassing
topological, algebraic, spectral, resistive, and
sensitivity analyses. Throughout our theoretic
elaborations we especially emphasize the practical
applicability of our results.},
doi = {10.1109/TCSI.2012.2215780},
}
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publisher = {Springer},
title = {Linear and Nonlinear Programming},
year = {2008},
isbn = {9780387745022},
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@book{SB-LEG-EF-VB:94,
author = {S. Boyd and L. {El~Ghaoui} and E. Feron and
V. Balakrishnan},
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Theory},
year = {1994},
isbn = {089871334X},
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@article{ZL-ZD-GC-LH:10,
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journal = {IEEE Transactions on Circuits and Systems~I: Regular
Papers},
number = {1},
pages = {213--224},
title = {Consensus of multiagent systems and synchronization
of complex networks: A unified viewpoint},
volume = {57},
year = {2010},
doi = {10.1109/TCSI.2009.2023937},
}
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author = {R. A. Horn and C. R. Johnson},
publisher = {Cambridge University Press},
title = {Topics in Matrix Analysis},
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isbn = {0521467136},
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@article{CFVL:85,
author = {Charles F. {Van~Loan}},
journal = {Journal of Computational and Applied Mathematics},
number = {1},
pages = {85-100},
title = {The ubiquitous {Kronecker} product},
volume = {123},
year = {2000},
abstract = {The Kronecker product has a rich and very pleasing
algebra that supports a wide range of fast, elegant,
and practical algorithms. Several trends in
scientific computing suggest that this important
matrix operation will have an increasingly greater
role to play in the future. First, the application
areas where Kronecker products abound are all
thriving. These include signal processing, image
processing, semidefinite programming, and quantum
computing. Second, sparse factorizations and
Kronecker products are proving to be a very effective
way to look at fast linear transforms. Researchers
have taken the Kronecker methodology as developed for
the fast Fourier transform and used it to build
exciting alternatives. Third, as computers get more
powerful, researchers are more willing to entertain
problems of high dimension and this leads to
Kronecker products whenever low-dimension techniques
are “tensored” together.},
doi = {10.1016/S0377-0427(00)00393-9},
}
@book{AJL:05,
author = {A. J. Laub},
publisher = {SIAM},
title = {Matrix Analysis for Scientists and Engineers},
year = {2005},
isbn = {0898717906},
}
@article{CWW-LOC:95,
author = {C. W. Wu and L. O. Chua},
journal = {IEEE Transactions on Circuits and Systems~I:
Fundamental Theory and Applications},
number = {10},
pages = {775-778},
title = {Application of {K}ronecker products to the analysis
of systems with uniform linear coupling},
volume = {42},
year = {1995},
doi = {10.1109/81.473586},
}
@article{TX-LS:16,
author = {T. Xia and L. Scardovi},
journal = {Systems \& Control Letters},
pages = {152-158},
title = {Output-feedback synchronizability of linear
time-invariant systems},
volume = {94},
year = {2016},
doi = {10.1016/j.sysconle.2016.06.007},
}
@article{EST:10,
author = {E. S. Tuna},
journal = {IEEE Transactions on Automatic Control},
number = {10},
pages = {2416-2420},
title = {Conditions for synchronizability in arrays of coupled
linear systems},
volume = {54},
year = {2012},
doi = {10.1109/TAC.2009.2029296},
}
@book{JHC:82,
editor = {Chow, J. H.},
publisher = {Springer},
series = {Lecture Notes in Control and Information Sciences},
title = {Time-Scale Modeling of Dynamic Networks with
Applications to Power Systems},
year = {1982},
isbn = {978-3-540-12106-0},
}
@article{JHC-PK:85,
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journal = {IEEE Transactions on Automatic Control},
number = {8},
pages = {714--722},
title = {Time scale modeling of sparse dynamic networks},
volume = {30},
year = {1985},
doi = {10.1109/TAC.1985.1104055},
}
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author = {Avramovic, B. and Kokotov\'ic, P. V. and
Winkelman, J. R. and Chow, J. H.},
journal = {Automatica},
number = {6},
pages = {637--648},
title = {Area decomposition for electromechanical models of
power systems},
volume = {16},
year = {1980},
doi = {10.1016/0005-1098(80)90006-0},
}
@article{JHC-JC-RAW:84,
author = {J. H. Chow and J. Cullum and R. A. Willoughby},
journal = {IEEE Transactions on Power Apparatus and Systems},
number = {3},
pages = {463--473},
title = {A sparsity-based technique for identifying
slow-coherent areas in large power systems},
volume = {103},
year = {1984},
doi = {10.1109/TPAS.1984.318724},
}
@article{VRS-JOR-PVK:84,
author = {V. R. Saksena and J. {O'Reilly} and
P. V. Kokotov\'ic},
journal = {Automatica},
number = {3},
pages = {273-293},
title = {Singular perturbations and time-scale methods in
control theory: {S}urvey 1976-1983},
volume = {20},
year = {1984},
doi = {10.1016/0005-1098(84)90044-X},
}
@inproceedings{WR-WA:05,
address = {San Francisco, CA, USA},
author = {W. Ren and W. Atkins},
booktitle = {AIAA Guidance, Navigation, and Control Conference and
Exhibit},
month = aug,
pages = {15-18},
title = {Second-order consensus protocols in multiple vehicle
systems with local interactions},
year = {2005},
doi = {10.2514/6.2005-6238},
}
@article{WR:08,
author = {W. Ren},
journal = {IEEE Transactions on Automatic Control},
number = {6},
pages = {1503-1509},
title = {On Consensus Algorithms for Double-integrator
Dynamics},
volume = {53},
year = {2008},
doi = {10.1109/TAC.2008.924961},
}
@article{WR:08b,
author = {W. Ren},
journal = {Automatica},
pages = {3196-3200},
title = {Synchronization of coupled harmonic oscillators with
local interaction},
volume = {44},
year = {2008},
doi = {10.1016/j.automatica.2008.05.027},
}
@article{JZ-YPT-JK:09,
author = {Zhu, J. and Tian, Y.P. and Kuang, J.},
journal = {Linear Algebra and its Applications},
number = {5-7},
pages = {701--715},
title = {On the general consensus protocol of multi-agent
systems with double-integrator dynamics},
volume = {431},
year = {2009},
doi = {10.1016/j.laa.2009.03.019},
}
@article{YZ-YPT:09,
author = {Y. Zhang and Y. P. Tian},
journal = {Automatica},
pages = {1195-1201},
title = {Consentability and protocol design of multi-agent
systems with stochastic switching topology},
volume = {45},
year = {2009},
doi = {10.1016/j.automatica.2008.11.005},
}
@article{WY-GC-MC:10,
author = {W. Yu and G. Chen and M. Cao},
journal = {Automatica},
number = {6},
pages = {1089-1095},
title = {Some necessary and sufficient conditions for
second-order consensus in multi-agent dynamical
systems},
volume = {46},
year = {2010},
doi = {10.1016/j.automatica.2010.03.006},
}
@article{JMM-GSS-GSS-FA:15,
author = {J. M. {Montenbruck} and G. S. {Schmidt} and
G. S. {Seyboth} and F. {Allgöwer}},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {3029-3034},
title = {On the Necessity of Diffusive Couplings in Linear
Synchronization Problems With Quadratic Cost},
volume = {60},
year = {2015},
abstract = {We show that diffusive couplings are necessary for
minimization of cost functionals integrating
quadratic synchronization error and quadratic input
signals. This holds for identical linear systems with
eigenvalues either on the imaginary axis or in the
open left half-plane, whilst for eigenvalues in the
open right half-plane, we present a counterexample in
which the strong solution to the associated algebraic
Riccati equation is not diffusive. For nonidentical
systems satisfying the internal model principle for
synchronization, we show that a certain part of the
coupling must be diffusive. For equally chosen
weights in the cost functional, we show that the
dimension of the associated algebraic Riccati
equation can be reduced significantly.},
doi = {10.1109/TAC.2015.2406971},
}
@article{HJvW-MKC-HLT:17,
author = {H. J. van~Waarde and M. K. Camlibel and
H. L. Trentelman},
journal = {IEEE Transactions on Automatic Control},
number = {6},
pages = {3099-3101},
title = {Comments on {“On the necessity of diffusive
couplings in linear synchronization problems with
quadratic cost”}},
volume = {62},
year = {2017},
doi = {10.1109/TAC.2017.2673246},
}
@article{PL-HKF:72,
author = {P. Lancaster and H. K. Farahat},
journal = {Mathematics of Computation},
number = {118},
pages = {401-414},
publisher = {American Mathematical Society},
title = {Norms on Direct Sums and Tensor Products},
volume = {26},
year = {1972},
doi = {10.2307/2005167},
}
@article{CW-RP-MM-JJES:20,
author = {C. Wu and R. Pines and M. Margaliot and
J.-J. E. Slotine},
journal = {IEEE Transactions on Automatic Control},
title = {Generalization of the multiplicative and additive
compounds of square matrices and contraction in the
{Hausdorff} dimension},
year = {2022},
doi = {10.1109/TAC.2022.3162547},
}
@article{GS:60,
author = {G. Sabidussi},
journal = {Mathematische Zeitschrift},
pages = {446-457},
title = {Graph multiplication},
volume = {72},
year = {1960},
doi = {10.1007/BF01162967},
}
@article{GS:93,
author = {G. Strang},
journal = {American Mathematical Monthly},
number = {9},
pages = {848--855},
title = {The fundamental theorem of linear algebra},
volume = {100},
year = {1993},
doi = {10.2307/2324660},
}
@article{GFO-CAD:71,
author = {G. F. Oster and C. A. Desoer},
journal = {Journal of Theoretical Biology},
number = {2},
pages = {219-241},
title = {Tellegen's theorem and thermodynamic inequalities},
volume = {32},
year = {1971},
abstract = {Electrical networks are special types of irreversible
thermodynamic systems. The underlying mathematical
unity of the two fields allows many of the techniques
of network analysis to be generalized, thus
permitting a wide class of non-linear,
non-steady-state irreversible processes to be
formulated in a network theoretic framework. One of
the most powerful of the network theorems is
Tellegen's theorem. Most, if not all, of the energy
distribution theorems and extremum principles can be
derived from it. In the following presentation we
will derive several thermodynamic inequalities as
well as explicit conditions guaranteeing the
stability or the unstability of an equilibrium point,
or a steady state.},
doi = {10.1016/0022-5193(71)90162-7},
}
@book{LRF:95,
author = {L. R. Foulds},
publisher = {Springer},
title = {Graph Theory Applications},
year = {1995},
isbn = {0387975993},
}
@article{NB:97,
author = {N. Biggs},
journal = {Bulletin of the London Mathematical Society},
number = {6},
pages = {641--682},
title = {Algebraic potential theory on graphs},
volume = {29},
year = {1997},
doi = {10.1112/S0024609397003305},
}
@article{SB-SDF-LS-DV:10,
author = {S. Bolognani and S. {Del~Favero} and L. Schenato and
D. Varagnolo},
journal = {International Journal of Robust and Nonlinear
Control},
number = {2},
pages = {176--193},
title = {Consensus-based distributed sensor calibration and
least-square parameter identification in {WSN}s},
volume = {20},
year = {2010},
doi = {10.1002/rnc.1452},
}
@phdthesis{DZ:09,
author = {D. Zelazo},
month = aug,
school = {University of Washington},
title = {Graph-Theoretic Methods for the Analysis and
Synthesis of Networked Dynamic Systems},
year = {2009},
}
@article{DZ-MM:11,
author = {D. Zelazo and M. Mesbahi},
journal = {IEEE Transactions on Automatic Control},
number = {3},
pages = {544--555},
title = {Edge agreement: {G}raph-theoretic performance bounds
and passivity analysis},
volume = {56},
year = {2011},
doi = {10.1109/TAC.2010.2056730},
}
@article{DZ-SS-FA:13,
author = {D. Zelazo and S. Schuler and F. Allg{\"o}wer},
journal = {Systems \& Control Letters},
number = {1},
pages = {85--96},
title = {Performance and design of cycles in consensus
networks},
volume = {62},
year = {2013},
doi = {10.1016/j.sysconle.2012.10.014},
}
@article{PB-JPH:07,
author = {P. Barooah and J. P. Hespanha},
journal = {{IEEE} Control Systems},
number = {4},
pages = {57-74},
title = {Estimation on graphs from relative measurements},
volume = {27},
year = {2007},
doi = {10.1109/MCS.2007.384125},
}
@article{PB-JPH:08,
author = {P. Barooah and J. P. Hespanha},
journal = {IEEE Transactions on Signal Processing},
number = {6},
pages = {2181--2193},
title = {Estimation from relative measurements: {E}lectrical
analogy and large graphs},
volume = {56},
year = {2008},
doi = {10.1109/TSP.2007.912270},
}
@article{GP-IS-BF-FB-BDOA:09r,
author = {G. Piovan and I. Shames and B. Fidan and F. Bullo and
B. D. O. Anderson},
journal = {Automatica},
number = {1},
pages = {206-213},
title = {On Frame and Orientation Localization for Relative
Sensing Networks},
volume = {49},
year = {2013},
doi = {10.1016/j.automatica.2012.09.014},
}
@article{TK-CL-KM-DM-RR-TU-KZ:09,
author = {T. Kavitha and C. Liebchen and K. Mehlhorn and
D. Michail and R. Rizzi and T. Ueckerdt and
K. A. Zweig},
journal = {Computer Science Review},
number = {4},
pages = {199-243},
title = {Cycle bases in graphs characterization, algorithms,
complexity, and applications},
volume = {3},
year = {2009},
abstract = {Abstract Cycles in graphs play an important role in
many applications, e.g., analysis of electrical
networks, analysis of chemical and biological
pathways, periodic scheduling, and graph drawing.
From a mathematical point of view, cycles in graphs
have a rich structure. Cycle bases are a compact
description of the set of all cycles of a graph. In
this paper, we survey the state of knowledge on cycle
bases and also derive some new results. We introduce
different kinds of cycle bases, characterize them in
terms of their cycle matrix, and prove structural
results and a priori length bounds. We provide
polynomial algorithms for the minimum cycle basis
problem for some of the classes and prove
APX-hardness for others. We also discuss three
applications and show that they require different
kinds of cycle bases.},
doi = {10.1016/j.cosrev.2009.08.001},
}
@article{MB-GHG-JL:05,
author = {M. Benzi and G. H. Golub and J. Liesen},
journal = {Acta Numerica},
pages = {1--137},
title = {Numerical solution of saddle point problems},
volume = {14},
year = {2005},
doi = {10.1017/S0962492904000212},
}
@article{AC-BG-JC:17,
author = {A. Cherukuri and B. Gharesifard and J. Cortes},
journal = {SIAM Journal on Control and Optimization},
number = {1},
pages = {486-511},
title = {Saddle-point dynamics: {Conditions} for asymptotic
stability of saddle points},
volume = {55},
year = {2017},
abstract = {This paper considers continuously differentiable
functions of two vector variables that have (possibly
a continuum of) min-max saddle points. We study the
asymptotic convergence properties of the associated
saddle-point dynamics (gradient descent in the first
variable and gradient ascent in the second one). We
identify a suite of complementary conditions under
which the set of saddle points is asymptotically
stable under the saddle-point dynamics. Our first set
of results is based on the convexity-concavity of the
function defining the saddle-point dynamics to
establish the convergence guarantees. For functions
that do not enjoy this feature, our second set of
results relies on properties of the linearization of
the dynamics, the function along the proximal normals
to the saddle set, and the linearity of the function
in one variable. We also provide global versions of
the asymptotic convergence results. Various examples
illustrate our discussion.},
doi = {10.1137/15M1026924},
}
@article{RBB:97,
author = {R. B. Bapat},
journal = {Linear and Multilinear Algebra},
number = {2},
pages = {159-167},
title = {{Moore-Penrose} inverse of the incidence matrix of a
tree},
volume = {42},
year = {1997},
abstract = {Let T be a tree with n vertices, where each edge is
given an orientation, and let Q be its vertex-edge
incidence matrix. It is shown that the Moore-Penrose
inverse of Q is the (n-1)x(n) matrix M obtained as
follows. The rows and the columns of M are indexed by
the edges and the vertices of T respectively. If e,v
are an edge and a vertex of T respectively, then the
(e,v)-entry of M is, upto a sign, the number of
vertices in the connected component of T\e which does
not contain v. Furthermore, the sign of the entry is
positive or negative, depending on whether e is
oriented away from or towards v. This result is then
used to obtain an expression for the Moore-Penrose
inverse of the incidence matrix of an arbitrary
directed graph. A recent result due to Moon is also
derived as a consequence.},
doi = {10.1080/03081089708818496},
}
@article{MD-VR:94,
author = {M. Desai and V. Rao},
journal = {Journal of Graph Theory},
number = {2},
pages = {181--194},
title = {A characterization of the smallest eigenvalue of a
graph},
volume = {18},
year = {1994},
doi = {10.1002/jgt.3190180210},
}
@article{DC-SSK:09,
author = {D. Cvetkovi{\'c} and S. K. Simi{\'c}},
journal = {Publications de l'Institut Mathematique},
number = {99},
pages = {19--33},
title = {Towards a spectral theory of graphs based on the
signless {Laplacian}, {I}},
volume = {85},
year = {2009},
doi = {10.2298/PIM0999019C},
}
@article{CB-DF-XM-IP:03,
author = {Balbuena, C. and Ferrero, D. and Marcote, X. and
Pelayo, I.},
journal = {Journal of Interconnection Networks},
number = {04},
pages = {377-393},
title = {Algebraic properties of a digraph and its line
digraph},
volume = {04},
year = {2003},
abstract = {Let G be a digraph, LG its line digraph and A(G) and
A(LG) their adjacency matrices. We present relations
between the Jordan Normal Form of these two matrices.
In addition, we study the spectra of those matrices
and obtain a relationship between their
characteristic polynomials that allows us to relate
properties of G and LG, specifically the number of
cycles of a given length.},
doi = {10.1142/S0219265903000933},
}
@article{SJ-FB:16h,
author = {S. Jafarpour and F. Bullo},
journal = {IEEE Transactions on Automatic Control},
number = {7},
pages = {2830-2844},
title = {Synchronization of {K}uramoto Oscillators via Cutset
Projections},
volume = {64},
year = {2019},
abstract = {Synchronization coupled oscillators networks is a
remarkable phenomenon of relevance in numerous
fields. A key question is how to characterize the
transition from synchrony to incoherence. For
Kuramoto oscillators the loss of synchronization is
determined by a trade-off between coupling strength
and oscillator heterogeneity. Despite extensive prior
work, the existing sufficient conditions for
synchronization are either very conservative or
heuristic and approximate. This paper proposes a
novel approach to the study of Kuramoto oscillators
based on an oblique projection operator, called the
cutset projection. We propose a novel family of
sufficient synchronization conditions; these
conditions rigorously identify the correct functional
form of the trade-off between coupling strength and
oscillator heterogeneity. To overcome the need to
solve a nonconvex optimization problem, we then
provide two explicit bounding methods, thereby
obtaining (i) the best-known sufficient condition
based on the 2-norm, and (ii) the first-know
generally-applicable sufficient condition based on
the $\infty$-norm. We conclude with a comparative
study of the novel conditions for specific topologies
and IEEE test cases; for IEEE test cases our new
sufficient conditions are always more accurate, in
most cases by one to two orders of magnitude, than
previous rigorous tests.},
doi = {10.1109/TAC.2018.2876786},
}
@book{GGW-MC:99,
author = {G. G. Walter and M. Contreras},
publisher = {Birkh{\"a}user},
title = {Compartmental Modeling with Networks},
year = {1999},
doi = {10.1007/978-1-4612-1590-5},
isbn = {0817640193},
}
@article{HWH:00,
author = {H. W. Hethcote},
journal = {SIAM Review},
number = {4},
pages = {599--653},
title = {The Mathematics of Infectious Diseases},
volume = {42},
year = {2000},
doi = {10.1137/S0036144500371907},
}
@article{WM-SM-SZ-FB:16f,
author = {W. Mei and S. Mohagheghi and S. Zampieri and
F. Bullo},
journal = {Annual Reviews in Control},
pages = {116-128},
title = {On the Dynamics of Deterministic Epidemic Propagation
over Networks},
volume = {44},
year = {2017},
abstract = {In this work we review a class of deterministic
nonlinear models for the propagation of infectious
diseases over contact networks with
strongly-connected topologies. We consider network
models for susceptible-infected (SI),
susceptible-infected-susceptible (SIS), and
susceptible-infected-recovered (SIR) settings. In
each setting, we provide a comprehensive nonlinear
analysis of equilibria, stability properties,
convergence, monotonicity, positivity, and threshold
conditions. For the network SI setting, specific
contributions include establishing its equilibria,
stability, and positivity properties. For the network
SIS setting, we review a well- known deterministic
model, provide novel results on the computation and
characterization of the endemic state (when the
system is above the epidemic threshold), and present
alternative proofs for some of its properties.
Finally, for the network SIR setting, we propose
novel results for transient behavior, threshold
conditions, stability properties, and asymptotic
convergence. These results are analogous to those
well-known for the scalar case. In addition, we
provide a novel iterative algorithm to compute the
asymptotic state of the network SIR system.},
doi = {10.1016/j.arcontrol.2017.09.002},
}
@article{NDC-PTM-CP:78,
author = {N. D. Charkes and P. T. Makler~Jr and C. Philips},
journal = {Journal of Nuclear Medicine},
number = {12},
pages = {1301--1309},
title = {Studies of skeletal tracer kinetics. {I.}
{D}igital-computer solution of a five-compartment
model of [18F] fluoride kinetics in humans.},
volume = {19},
year = {1978},
}
@article{PvdD-JW:02,
author = {P. Van~den~Driessche and J. Watmough},
journal = {Mathematical Biosciences},
number = {1},
pages = {29-48},
title = {Reproduction numbers and sub-threshold endemic
equilibria for compartmental models of disease
transmission},
volume = {180},
year = {2002},
abstract = {A precise definition of the basic reproduction
number, R0, is presented for a general compartmental
disease transmission model based on a system of
ordinary differential equations. It is shown that, if
R0<1, then the disease free equilibrium is locally
asymptotically stable; whereas if R0>1, then it is
unstable. Thus, R0 is a threshold parameter for the
model. An analysis of the local centre manifold
yields a simple criterion for the existence and
stability of super- and sub-threshold endemic
equilibria for R0 near one. This criterion, together
with the definition of R0, is illustrated by
treatment, multigroup, staged progression,
multistrain and vector-host models and can be applied
to more complex models. The results are significant
for disease control.},
doi = {10.1016/S0025-5564(02)00108-6},
}
@book{RSV:62,
author = {R. S. Varga},
publisher = {Prentice Hall},
title = {Matrix Iterative Analysis},
year = {1962},
isbn = {0135655072},
}
@article{SD-HI-FRW:11,
author = {S. Dashkovskiy and H. Ito and F. R. Wirth},
journal = {European Journal of Control},
pages = {1-9},
title = {On a Small Gain Theorem for {ISS} Networks in
Dissipative {Lyapunov} form},
volume = {4},
year = {2011},
doi = {10.3166/ejc.17.357-365},
}
@article{KDS-FB:21i,
author = {K. D. Smith and F. Bullo},
journal = {IEEE Transactions on Automatic Control},
number = {7},
pages = {4398-4404},
title = {Convex Optimization of the Basic Reproduction Number},
volume = {68},
year = {2023},
doi = {10.1109/TAC.2022.3212012},
}
@article{RS-KSN:09,
author = {R. Shorten and K. S. Narendra},
journal = {Linear Algebra and its Applications},
number = {12},
pages = {2317-2329},
title = {On a theorem of {Redheffer} concerning diagonal
stability},
volume = {431},
year = {2009},
abstract = {An important problem in system theory concerns
determining whether or not a given LTI system x˙=Ax
is diagonally stable. More precisely, this problem is
concerned with determining conditions on a matrix A
such that there exists a diagonal matrix D with
positive diagonal entries (i.e. a positive diagonal
matrix), satisfying ATD+DA=-Q<0. While this problem
has attracted much attention over the past half
century, two results of note stand out: (i) a result
based on Theorems of the Alternative derived by
Barker, Berman and Plemmons; and (ii) algebraic
conditions derived by Redheffer. This paper is
concerned with the second of these conditions. Our
principal contribution is to show that Redheffer’s
result can be obtained from the
Kalman-Yacubovich-Popov lemma. We then show that this
method of proof leads to natural generalisations of
Redheffer’s result and we use these results to
derive new conditions for diagonal and Hurwitz
stability for special classes of matrices.},
doi = {10.1016/j.laa.2009.02.035},
}
@article{YE-DP-DA:17,
author = {Y. Ebihara and D. Peaucelle and D. Arzelier},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {652-667},
title = {Analysis and Synthesis of Interconnected Positive
Systems},
volume = {62},
year = {2017},
abstract = {This paper is concerned with the analysis and
synthesis of interconnected systems constructed from
heterogeneous positive subsystems and a nonnegative
interconnection matrix. We first show that
admissibility, to be defined in this paper, is an
essential requirement in constructing such
interconnected systems. Then, we clarify that the
interconnected system is admissible and stable if and
only if a Metzler matrix, which is built from the
coefficient matrices of positive subsystems and the
nonnegative interconnection matrix, is Hurwitz
stable. By means of this key result, we further
provide several results that characterize the
admissibility and stability of the interconnected
system in terms of the Frobenius eigenvalue of the
interconnection matrix and the weighted L1- induced
norm of the positive subsystems again to be defined
in this paper. Moreover, in the case where every
subsystem is SISO, we provide explicit conditions
under which the interconnected system has the
property of persistence, i.e., its state converges to
a unique strictly positive vector (that is known in
advance up to a strictly positive constant
multiplicative factor) for any nonnegative and
nonzero initial state. As an important consequence of
this property, we show that the output of the
interconnected system converges to a scalar multiple
of the right eigenvector of a nonnegative matrix
associated with its Frobenius eigenvalue, where the
nonnegative matrix is nothing but the interconnection
matrix scaled by the steady-stage gains of the
positive subsystems. This result is then naturally
and effectively applied to formation control of
multiagent systems with positive dynamics. This
result can be seen as a generalization of a
well-known consensus algorithm that has been
basically applied to interconnected systems
constructed from integrators.},
doi = {10.1109/TAC.2016.2558287},
}
@article{HH-JQ:73,
author = {H. Habibagahi and J. Quirk},
journal = {Review of Economic Studies},
number = {2},
pages = {249--258},
title = {Hicksian Stability and {Walras'} Law},
volume = {40},
year = {1973},
doi = {10.2307/2296651},
}
@book{LF-SR:00,
author = {L. Farina and S. Rinaldi},
publisher = {John Wiley \& Sons},
title = {Positive Linear Systems: Theory and Applications},
year = {2000},
isbn = {0471384569},
}
@article{AVdS:15,
author = {A. J. van der Schaft},
journal = {Systems \& Control Letters},
title = {Modeling of physical network systems},
year = {2015},
abstract = {Conservation laws and balance equations for physical
network systems typically can be described with the
aid of the incidence matrix of a directed graph, and
an associated symmetric Laplacian matrix. Some basic
examples are discussed, and the extension to k
-complexes is indicated. Physical distribution
networks often involve a non-symmetric Laplacian
matrix. It is shown how, in case the connected
components of the graph are strongly connected, such
systems can be converted into a form with balanced
Laplacian matrix by constructive use of Kirchhoff’s
Matrix Tree theorem, giving rise to a
port-Hamiltonian description. Application to the dual
case of asymmetric consensus algorithms is given.
Finally it is shown how the minimal storage function
for physical network systems with controlled flows
can be explicitly computed.},
doi = {10.1016/j.sysconle.2015.08.013},
}
@incollection{AJvdS-JW:12,
author = {A. J. van der Schaft and J. Wei},
booktitle = {Lagrangian and Hamiltonian Methods for Nonlinear
Control 2012},
pages = {24-29},
publisher = {Elsevier},
title = {A {H}amiltonian perspective on the control of
dynamical distribution networks},
year = {2012},
doi = {10.3182/20120829-3-IT-4022.00033},
}
@book{TK:01,
author = {T. Kaczorek},
publisher = {Springer},
title = {Positive 1D and 2D Systems},
year = {2001},
doi = {10.1007/978-1-4471-0221-2},
}
@article{KSN-RS:10,
author = {K. S. Narendra and R. Shorten},
journal = {IEEE Transactions on Automatic Control},
number = {6},
pages = {1484--1487},
title = {Hurwitz stability of {M}etzler matrices},
volume = {55},
year = {2010},
doi = {10.1109/TAC.2010.2045694},
}
@article{FB-PC-MEV:12,
author = {F. Blanchini and P. Colaneri and M. E. Valcher},
journal = {IEEE Transactions on Automatic Control},
number = {12},
pages = {3038-3050},
title = {Co-Positive {Lyapunov} Functions for the
Stabilization of Positive Switched Systems},
volume = {57},
year = {2012},
doi = {10.1109/TAC.2012.2199169},
}
@article{ZM-WX-KHJ-SH:17,
author = {Z. {Meng} and W. {Xia} and K. H. {Johansson} and
S. {Hirche}},
journal = {IEEE Transactions on Automatic Control},
number = {1},
pages = {399-405},
title = {Stability of Positive Switched Linear Systems: {W}eak
Excitation and Robustness to Time-Varying Delay},
volume = {62},
year = {2017},
doi = {10.1109/TAC.2016.2531044},
}
@article{XD-SJ-FB:19f,
author = {X. Duan and S. Jafarpour and F. Bullo},
journal = {SIAM Journal on Control and Optimization},
number = {5},
pages = {3447-3471},
title = {Graph-Theoretic Stability Conditions for {Metzler}
Matrices and Monotone Systems},
volume = {59},
year = {2021},
abstract = {This paper studies the graph-theoretic conditions for
stability of positive monotone systems. Using
concepts from the input-to-state stability and
network small-gain theory, we first establish
necessary and sufficient conditions for the stability
of linear positive systems described by Metzler
matrices. Specifically, we define and compute two
forms of input-to-state stability gains for Metzler
systems, namely max-interconnection gains and
sum-interconnection gains. Then, based on the
max-interconnection gains, we show that the cyclic
small-gain theorem becomes necessary and sufficient
for the stability of Metzler systems; based on the
sum-interconnection gains, we obtain novel
graph-theoretic conditions for the stability of
Metzler systems. All these conditions highlight the
role of cycles in the interconnection graph and
unveil how the structural properties of the graph
affect stability. Finally, we extend our results to
the nonlinear monotone system and obtain similar
sufficient conditions for global asymptotic
stability.},
doi = {10.1137/20M131802X},
}
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@book{WMH-VC-GH:10,
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year = {2010},
isbn = {0691144117},
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@article{GC-KS-DA-MAD-EF:13,
author = {G. Como and K. Savla and D. Acemoglu and M. A. Dahleh and
E. Frazzoli},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {317-332},
title = {Robust distributed routing in dynamical networks --
{Part I: L}ocally responsive policies and weak
resilience},
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year = {2013},
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}
@article{SC-MA:15,
author = {S. Coogan and M. Arcak},
journal = {IEEE Transactions on Automatic Control},
number = {10},
pages = {2698--2703},
title = {A compartmental model for traffic networks and its
dynamical behavior},
volume = {60},
year = {2015},
abstract = {We propose a macroscopic traffic network flow model
suitable for analysis as a dynamical system, and we
qualitatively analyze equilibrium flows as well as
convergence. Flows at a junction are determined by
downstream supply of capacity as well as upstream
demand of traffic wishing to flow through the
junction. This approach is rooted in the celebrated
Cell Transmission Model for freeway traffic flow.
Unlike related results which rely on certain system
cooperativity properties, our model generally does
not possess these properties. We show that the lack
of cooperativity is in fact a useful feature that
allows traffic control methods, such as ramp
metering, to be effective. Finally, we leverage the
results of the technical note to develop a linear
program for optimal ramp metering.},
doi = {10.1109/TAC.2015.2411916},
}
@article{EDS:07,
author = {E. D. Sontag},
journal = {Systems and Synthetic Biology},
number = {2},
pages = {59--87},
title = {Monotone and near-monotone biochemical networks},
volume = {1},
year = {2007},
abstract = {Monotone subsystems have appealing properties as
components of larger networks, since they exhibit
robust dynamical stability and predictability of
responses to perturbations. This suggests that
natural biological systems may have evolved to be, if
not monotone, at least close to monotone in the sense
of being decomposable into a ``small'' number of
monotone components, In addition, recent research has
shown that much insight can be attained from
decomposing networks into monotone subsystems and the
analysis of the resulting interconnections using
tools from control theory. This paper provides an
expository introduction to monotone systems and their
interconnections, describing the basic concepts and
some of the main mathematical results in a largely
informal fashion.},
doi = {10.1007/s11693-007-9005-9},
}
@misc{QM-YYL-AO:22,
author = {Q. Ma and Y.-Y. Liu and A. Olshevsky},
title = {Optimal Lockdown for Pandemic Control},
year = {2022},
url = {http://arxiv.org/abs/2010.12923},
}
@article{MP-SS:16,
author = {M. Pirani and S. Sundaram},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {509-514},
title = {On the Smallest Eigenvalue of Grounded {L}aplacian
Matrices},
volume = {61},
year = {2016},
doi = {10.1109/TAC.2015.2444191},
}
@article{WX-MC:17,
author = {W. Xia and M. Cao},
journal = {Automatica},
pages = {10-16},
title = {Analysis and applications of spectral properties of
grounded {L}aplacian matrices for directed networks},
volume = {80},
year = {2017},
doi = {10.1016/j.automatica.2017.01.009},
}
@article{LX-SB:04,
author = {L. Xiao and S. Boyd},
journal = {Systems \& Control Letters},
pages = {65-78},
title = {Fast linear iterations for distributed averaging},
volume = {53},
year = {2004},
doi = {10.1016/j.sysconle.2004.02.022},
}
@misc{MG-SB:11-cvx,
author = {M. Grant and S. Boyd},
month = mar,
title = {{CVX}: Matlab Software for Disciplined Convex
Programming, version 2.1},
year = {2014},
url = {http://cvxr.com/cvx},
}
@unpublished{FF:14,
author = {F. Fagnani},
month = jan,
note = {Lecture notes for Winter School on Complex Networks,
INRIA. Downloaded on 12/23/2016},
title = {Consensus dynamics over networks},
year = {2014},
url = {http://www-sop.inria.fr/members/Giovanni.Neglia/
complexnetworks14},
}
@article{JC:06b,
author = {J. Cort{\'e}s},
journal = {Automatica},
number = {11},
pages = {1993-2000},
title = {Finite-time convergent gradient flows with
applications to network consensus},
volume = {42},
year = {2006},
doi = {10.1016/j.automatica.2006.06.015},
}
@article{LW-FX:10,
author = {L. Wang and F. Xiao},
journal = {IEEE Transactions on Automatic Control},
number = {4},
pages = {950--955},
title = {Finite-time consensus problems for networks of
dynamic agents},
volume = {55},
year = {2010},
doi = {10.1109/TAC.2010.2041610},
}
@article{AO:17,
author = {A. Olshevsky},
journal = {SIAM Journal on Control and Optimization},
number = {6},
pages = {3990-4014},
title = {Linear Time Average Consensus and Distributed
Optimization on Fixed Graphs},
volume = {55},
year = {2017},
doi = {10.1137/16M1076629},
}
@inproceedings{RC-FG-SZ:09,
address = {San Diego, USA},
author = {R. Carli and F. Garin and S. Zampieri},
booktitle = {IEEE Information Theory and Applications Workshop},
month = feb,
pages = {96--104},
title = {Quadratic indices for the analysis of consensus
algorithms},
year = {2009},
doi = {10.1109/ITA.2009.5044929},
}
@article{RC-FF-AS-SZ:08,
author = {R. Carli and F. Fagnani and A. Speranzon and
S. Zampieri},
journal = {Automatica},
number = {3},
pages = {671-684},
title = {Communication constraints in the average consensus
problem},
volume = {44},
year = {2008},
abstract = {The rendezvous problem can be seen as the simplest
instance of coordinated control of autonomous agents.
This problem has been widely investigated in the
recent years. It is clear that the information
exchange must have an important influence on the
performance of the control strategy. In this
contribution the information flow is modelled by a
graph representing the information transmission from
one vehicle to another one. In this graph there exist
two kinds of edges. One kind represents the exact
data transmission. This is very expensive with
respect to the communication rate required. A second
kind of edges represents the transmission logarithmic
quantized data. On the contrary this is very cheap
with respect to communication rate required. The
final goal of the present paper is to determine how
the degree of connection of this graph influences the
performance of the coordinated control system.},
doi = {10.1016/j.automatica.2007.07.009},
}
@article{BP:64,
author = {B. T. Polyak},
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Physics},
number = {5},
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iteration methods},
volume = {4},
year = {1964},
doi = {10.1016/0041-5553(64)90137-5},
}
@article{SM-BG-MHS:98,
author = {S. Muthukrishnan and B. Ghosh and M. H. Schultz},
journal = {Theory of Computing Systems},
number = {4},
pages = {331--354},
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coarse, distributed load balancing},
volume = {31},
year = {1998},
doi = {10.1007/s002240000092},
}
@inproceedings{NB-RC-LS:16,
address = {Aalborg, Denmark},
author = {N. Bof and R. Carli and L. Schenato},
booktitle = {{E}uropean {C}ontrol {C}onference},
month = jun,
pages = {160--165},
title = {On the performance of consensus based versus
{L}agrangian based algorithms for quadratic cost
functions},
year = {2016},
doi = {10.1109/ECC.2016.7810280},
}
@inproceedings{GFY-LS-NEL:10,
address = {Baltimore, USA},
author = {G. F. Young and L. Scardovi and N. E. Leonard},
booktitle = {{A}merican {C}ontrol {C}onference},
pages = {6312--6317},
title = {Robustness of noisy consensus dynamics with directed
communication},
year = {2010},
abstract = {In this paper we study robustness of consensus in
networks of coupled single integrators driven by
white noise. Robustness is quantified as the H2 norm
of the closed-loop system. In particular we
investigate how robustness depends on the properties
of the underlying (directed) communication graph. To
this end several classes of directed and undirected
communication topologies are analyzed and compared.
The trade-off between speed of convergence and
robustness to noise is also investigated.},
doi = {10.1109/ACC.2010.5531506},
}
@phdthesis{JMH:08,
author = {J. M. Hendrickx},
month = feb,
school = {Departement d'Ingenierie Mathematique, Universit{\'e}
Catholique de Louvain, Belgium},
title = {Graphs and Networks for the Analysis of Autonomous
Agent Systems},
year = {2008},
annote = {Available at
\textt{http://perso.uclouvain.be/julien.hendrickx}},
}
@article{LM:05,
author = {L. Moreau},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {169-182},
title = {Stability of multiagent systems with time-dependent
communication links},
volume = {50},
year = {2005},
abstract = {We study a simple but compelling model of network of
agents interacting via time-dependent communication
links. The model finds application in a variety of
fields including synchronization, swarming and
distributed decision making. In the model, each agent
updates his current state based upon the current
information received from neighboring agents.
Necessary and/or sufficient conditions for the
convergence of the individual agentsÃ states to a
common value are presented, thereby extending recent
results reported in the literature. The stability
analysis is based upon a blend of graph-theoretic and
system-theoretic tools with the notion of convexity
playing a central role. The analysis is integrated
within a formal framework of set-valued Lyapunov
theory, which may be of independent interest. Among
others, it is observed that more communication does
not necessarily lead to faster convergence and may
eventually even lead to a loss of convergence, even
for the simple models discussed in the present
paper.},
doi = {10.1109/TAC.2004.841888},
}
@article{VDB-AO:14,
author = {V. D. Blondel and A. Olshevsky},
journal = {SIAM Journal on Control and Optimization},
number = {5},
pages = {2707--2726},
title = {How to decide consensus? {A} combinatorial necessary
and sufficient condition and a proof that consensus
is decidable but {NP}-hard},
volume = {52},
year = {2014},
doi = {10.1137/12086594X},
}
@article{WX-MC:14,
author = {W. Xia and M. Cao},
journal = {IEEE Transactions on Automatic Control},
number = {8},
pages = {2228--2233},
title = {Sarymsakov matrices and asynchronous implementation
of distributed coordination algorithms},
volume = {59},
year = {2014},
doi = {10.1109/TAC.2014.2301571},
}
@phdthesis{JNT:84,
author = {J. N. Tsitsiklis},
month = nov,
school = {Massachusetts Institute of Technology},
title = {Problems in Decentralized Decision Making and
Computation},
year = {1984},
}
@article{JNT-DPB-MA:86,
author = {J. N. Tsitsiklis and D. P. Bertsekas and M. Athans},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {803-812},
title = {Distributed asynchronous deterministic and stochastic
gradient optimization algorithms},
volume = {31},
year = {1986},
abstract = {Asynchronous distributed iterative optimization
algorithms are modeled for the following cases in
which each processor does not need to communicate to
each other processor at each time instance:
processors may keep performing computations without
having to wait until they receive the messages that
have been transmitted to them; processors are allowed
to remain idle some of the time; some processors may
perform computations faster than others. A model for
asynchronous distributed computation is presented and
then the convergence of natural asynchronous
distributed versions of a large class of
deterministic and stochastic gradient-like algorithms
is analyzed. It is shown that such algorithms retain
the desirable convergence properties of their
centralized counterparts, provided that the time
between consecutive communications between processors
and communication delays is not too large. (19
References).},
doi = {10.1109/TAC.1986.1104412},
}
@article{YH-JH-LG:06,
author = {Y. Hong and J. Hu and L. Gao},
journal = {Automatica},
number = {7},
pages = {1177--1182},
title = {Tracking control for multi-agent consensus with an
active leader and variable topology},
volume = {42},
year = {2006},
doi = {10.1016/j.automatica.2006.02.013},
}
@article{YH-LG-DC-JH:07,
author = {Y. Hong and L. Gao and D. Cheng and J. Hu},
journal = {IEEE Transactions on Automatic Control},
number = {5},
pages = {943-948},
title = {Lyapunov-Based Approach to Multiagent Systems With
Switching Jointly Connected Interconnection},
volume = {52},
year = {2007},
doi = {10.1109/TAC.2007.895860},
}
@article{MC-ASM-BDOA:08,
author = {M. Cao and A. S. Morse and B. D. O. Anderson},
journal = {IEEE Transactions on Automatic Control},
number = {8},
pages = {1826--1838},
title = {Agreeing asynchronously},
volume = {53},
year = {2008},
doi = {10.1109/TAC.2008.929387},
}
@inproceedings{LM:04,
address = {Nassau, Bahamas},
author = {L. Moreau},
booktitle = {{IEEE} Conf.\ on Decision and Control},
month = dec,
pages = {3998--4003},
title = {Stability of continuous-time distributed consensus
algorithms},
year = {2004},
doi = {10.1109/CDC.2004.1429377},
}
@article{ZL-BF-MM:07,
author = {Z. Lin and B. Francis and M. Maggiore},
journal = {SIAM Journal on Control and Optimization},
number = {1},
pages = {288-307},
title = {State agreement for continuous-time coupled nonlinear
systems},
volume = {46},
year = {2007},
abstract = {Two related problems are treated in continuous time.
First, the state agreement problem is studied for
coupled nonlinear differential equations. The vector
fields can switch within a finite family. Associated
to each vector field is a directed graph based in a
natural way on the interaction structure of the
subsystems. Generalizing the work of Moreau, under
the assumption that the vector fields satisfy a
certain subtangentiality condition, it is proved that
asymptotic state agreement is achieved if and only if
the dynamic interaction digraph has the property of
being sufficiently connected over time. The proof
uses nonsmooth analysis. Second, the rendezvous
problem for kinematic point-mass mobile robots is
studied when the robotsÃ fields of view have a
fixed radius. The circumcenter control law of Ando et
al. [IEEE Trans. Robotics Automation, 15 (1999), pp.
818Ã 828] is shown to solve the problem. The
rendezvous problem is a kind of state agreement
problem, but the interaction structure is state
dependent.},
doi = {10.1137/050626405},
}
@article{JMH-JNT:13,
author = {J. M. Hendrickx and J. N. Tsitsiklis},
journal = {IEEE Transactions on Automatic Control},
number = {1},
pages = {214--218},
title = {Convergence of type-symmetric and cut-balanced
consensus seeking systems},
volume = {58},
year = {2013},
doi = {10.1109/TAC.2012.2203214},
}
@article{AJ-JL-ASM:02,
author = {A. Jadbabaie and J. Lin and A. S. Morse},
journal = {IEEE Transactions on Automatic Control},
number = {6},
pages = {988-1001},
title = {Coordination of groups of mobile autonomous agents
using nearest neighbor rules},
volume = {48},
year = {2003},
abstract = {In a recent Physical Review Letters article, Vicsek
et al. propose a simple but compelling discrete-time
model of n autonomous agents (i.e., points or
particles) all moving in the plane with the same
speed but with different headings. Each agent's
heading is updated using a local rule based on the
average of its own heading plus the headings of its
"neighbors." In their paper, Vicsek et al. provide
simulation results which demonstrate that the nearest
neighbor rule they are studying can cause all agents
to eventually move in the same direction despite the
absence of centralized coordination and despite the
fact that each agent's set of nearest neighbors
change with time as the system evolves. This paper
provides a theoretical explanation for this observed
behavior. In addition, convergence results are
derived for several other similarly inspired models.
The Vicsek model proves to be a graphic example of a
switched linear system which is stable, but for which
there does not exist a common quadratic Lyapunov
function.},
doi = {10.1109/TAC.2003.812781},
}
@article{FF-SZ:08a,
author = {F. Fagnani and S. Zampieri},
journal = {IEEE Journal on Selected Areas in Communications},
number = {4},
pages = {634-649},
title = {Randomized consensus algorithms over large scale
networks},
volume = {26},
year = {2008},
doi = {10.1109/JSAC.2008.080506},
}
@article{ATS-AJ:08,
author = {A. Tahbaz-Salehi and A. Jadbabaie},
journal = {IEEE Transactions on Automatic Control},
number = {3},
pages = {791-795},
title = {A necessary and sufficient condition for consensus
over random networks},
volume = {53},
year = {2008},
doi = {10.1109/TAC.2008.917743},
}
@article{SC-ES:77,
author = {S. Chatterjee and E. Seneta},
journal = {Journal of Applied Probability},
number = {1},
pages = {89-97},
title = {Towards Consensus: {S}ome Convergence Theorems on
Repeated Averaging},
volume = {14},
year = {1977},
annote = {The problem of tendency to consensus in an
information-exchanging operation is connected with
the ergodicity problem for backwards products of
stochastic matrices. For such products, weak and
strong ergodicity, defined analogously to these
concepts for forward products of inhomogeneous Markov
chain theory, are shown (in contrast to that theory)
to be equivalent. Conditions for ergodicity are
derived and their relation to the consensus problem
is considered.},
doi = {10.2307/3213262},
}
@article{RC:84,
author = {R. Cogburn},
journal = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie und
Verwandte Gebiete},
number = {1},
pages = {109-128},
title = {The ergodic theory of {M}arkov chains in random
environments},
volume = {66},
year = {1984},
doi = {10.1007/BF00532799},
}
@article{ATS-AJ:10,
author = {A. Tahbaz-Salehi and A. Jadbabaie},
journal = {IEEE Transactions on Automatic Control},
number = {1},
pages = {225--230},
title = {Consensus over ergodic stationary graph processes},
volume = {55},
year = {2010},
doi = {10.1109/TAC.2009.2034054},
}
@article{YH-MM:05,
author = {Y. Hatano and M. Mesbahi},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {1867-1872},
title = {Agreement over random networks},
volume = {50},
year = {2005},
doi = {10.1109/TAC.2005.858670},
}
@article{DB-JX-JMFM-BS:13,
author = {D. Bajovi{\'c} and J. Xavier and J. M. F. Moura and
B. Sinopoli},
journal = {IEEE Transactions on Signal Processing},
number = {10},
pages = {2557--2571},
title = {Consensus and products of random stochastic matrices:
Exact rate for convergence in probability},
volume = {61},
year = {2013},
doi = {10.1109/TSP.2013.2248003},
}
@article{IM-JSB-CS:13,
author = {I. Matei and J. S. Baras and C. Somarakis},
journal = {SIAM Journal on Control and Optimization},
number = {2},
pages = {1574--1591},
title = {Convergence results for the linear consensus problem
under {Markovian} random graphs},
volume = {51},
year = {2013},
doi = {10.1137/100816870},
}
@article{BT-AN:14,
author = {B. Touri and A. Nedi{\'c}},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {437--448},
title = {Product of random stochastic matrices},
volume = {59},
year = {2014},
doi = {10.1109/TAC.2013.2283750},
}
@article{PF-JMH:13,
author = {P. Frasca and J. M. Hendrickx},
journal = {Automatica},
number = {8},
pages = {2496-2501},
title = {On the mean square error of randomized averaging
algorithms},
volume = {49},
year = {2013},
abstract = {This paper considers randomized discrete-time
consensus systems that preserve the average “on
average”. As a main result, we provide an upper
bound on the mean square deviation of the consensus
value from the initial average. Then, we apply our
result to systems in which few or weakly correlated
interactions take place: these assumptions cover
several algorithms proposed in the literature. For
such systems we show that, when the network size
grows, the deviation tends to zero, and that the
speed of this decay is not slower than the inverse of
the size. Our results are based on a new approach,
which is unrelated to the convergence properties of
the system.},
doi = {10.1016/j.automatica.2013.04.035},
}
@article{SB-AG-BP-DS:06,
author = {S. Boyd and A. Ghosh and B. Prabhakar and D. Shah},
journal = {IEEE Transactions on Information Theory},
number = {6},
pages = {2508-2530},
title = {Randomized gossip algorithms},
volume = {52},
year = {2006},
doi = {10.1109/TIT.2006.874516},
}
@article{DA-AO:11,
author = {D. Acemoglu and A. Ozdaglar},
journal = {Dynamic Games and Applications},
number = {1},
pages = {3-49},
title = {Opinion Dynamics and Learning in Social Networks},
volume = {1},
year = {2011},
doi = {10.1007/s13235-010-0004-1},
}
@article{DA-GC-FF-AO:10,
author = {D. Acemoglu and G. Como and F. Fagnani and
A. Ozdaglar},
journal = {Mathematics of Operation Research},
number = {1},
pages = {1-27},
title = {Opinion fluctuations and disagreement in social
networks},
volume = {38},
year = {2013},
doi = {10.1287/moor.1120.0570},
}
@article{AK-TB-RS:07,
author = {A. Kashyap and T. Ba{\c s}ar and R. Srikant},
journal = {Automatica},
number = {7},
pages = {1192-1203},
title = {Quantized consensus},
volume = {43},
year = {2007},
doi = {10.1016/j.automatica.2007.01.002},
}
@article{AN-AO-AO-JNT:09,
author = {Nedi{\'c}, A. and Olshevsky, A. and Ozdaglar, A. and
Tsitsiklis, J. N.},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {2506-2517},
title = {On distributed averaging algorithms and quantization
effects},
volume = {54},
year = {2009},
doi = {10.1109/TAC.2009.2031203},
}
@article{PF-RC-FF-SZ:09,
author = {P. Frasca and R. Carli and F. Fagnani and
S. Zampieri},
journal = {International Journal of Robust and Nonlinear
Control},
number = {16},
pages = {1787--1816},
title = {Average consensus on networks with quantized
communication},
volume = {19},
year = {2009},
doi = {10.1002/rnc.1396},
}
@article{LX-SB-SJK:07,
author = {L. Xiao and S. Boyd and S.-J. Kim},
journal = {Journal of Parallel and Distributed Computing},
number = {1},
pages = {33-46},
title = {Distributed Average Consensus with Least-Mean-Square
Deviation},
volume = {67},
year = {2007},
doi = {10.1016/j.jpdc.2006.08.010},
}
@article{BB-MRJ-PM-SP:12,
author = {B. Bamieh and M. R. Jovanovic and P. Mitra and
S. Patterson},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {2235-2249},
title = {Coherence in Large-Scale Networks:
Dimension-Dependent Limitations of Local Feedback},
volume = {57},
year = {2012},
doi = {10.1109/TAC.2012.2202052},
}
@article{EL-FG-SZ:13,
author = {E. Lovisari and F. Garin and S. Zampieri},
journal = {SIAM Journal on Control and Optimization},
number = {5},
pages = {3918--3945},
title = {Resistance-based performance analysis of the
consensus algorithm over geometric graphs},
volume = {51},
year = {2013},
doi = {10.1137/110857428},
}
@article{AJ-AO:18,
author = {A. Jadbabaie and A. Olshevsky},
journal = {IEEE Transactions on Automatic Control},
number = {4},
pages = {1389-1402},
title = {Scaling laws for consensus protocols subject to
noise},
volume = {64},
year = {2019},
doi = {10.1109/TAC.2018.2863203},
}
@article{ROS-RMM:03c,
author = {R. Olfati-Saber and R. M. Murray},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {1520-1533},
title = {Consensus problems in networks of agents with
switching topology and time-delays},
volume = {49},
year = {2004},
doi = {10.1109/TAC.2004.834113},
}
@article{JH-YH:07,
author = {J. Hu and Y. Hong},
journal = {Physica A: Statistical Mechanics and its
Applications},
number = {2},
pages = {853-863},
title = {Leader-following coordination of multi-agent systems
with coupling time delays},
volume = {374},
year = {2007},
abstract = {In this paper, we consider a leader-following
consensus problem of a group of autonomous agents
with time-varying coupling delays. Two different
cases of coupling topologies are investigated. At
first, a necessary and sufficient condition is proved
in the case when the interconnection topology is
fixed and directed. Then a sufficient condition is
proposed in the case when the coupling topology is
switched and balanced. Numerical examples are also
given to illustrate our results.},
doi = {10.1016/j.physa.2006.08.015},
}
@article{PL-YJ:08,
author = {P. Lin and Y. Jia},
journal = {Physica A: Statistical Mechanics and its
Applications},
number = {1},
pages = {303-313},
title = {Average consensus in networks of multi-agents with
both switching topology and coupling time-delay},
volume = {387},
year = {2008},
abstract = {This paper is devoted to the study of the
average-consensus problem in directed networks of
agents with both switching topology and time-delay.
The stability analysis is performed based on a
proposed Lyapunov-Krasovskii function. Sufficient
conditions in terms of linear matrix inequalities
(LMIs) are given to guarantee the average consensus
under arbitrary switching of the network topology
even if the time-delay is time-varying. Numerical
simulations show the effectiveness of our theoretical
results.},
doi = {10.1016/j.physa.2007.08.040},
}
@article{AJL:1920,
author = {A. J. Lotka},
journal = {Proceedings of the National Academy of Sciences},
number = {7},
pages = {410-415},
title = {Analytical note on certain rhythmic relations in
organic systems},
volume = {6},
year = {1920},
doi = {10.1073/pnas.6.7.410},
}
@article{VV:1928,
author = {V. Volterra},
journal = {ICES Journal of Marine Science},
number = {1},
pages = {3--51},
publisher = {Oxford University Press},
title = {Variations and fluctuations of the number of
individuals in animal species living together},
volume = {3},
year = {1928},
doi = {10.1093/icesjms/3.1.3},
}
@book{EPO:59,
author = {E. P. Odum},
publisher = {Saunders Company},
title = {Fundamentals of Ecology},
year = {1959},
}
@incollection{YK:75,
author = {Y. Kuramoto},
booktitle = {Int. Symposium on Mathematical Problems in
Theoretical Physics},
editor = {H. Araki},
pages = {420-422},
publisher = {Springer},
series = {Lecture Notes in Physics},
title = {Self-entrainment of a population of coupled
non-linear oscillators},
volume = {39},
year = {1975},
doi = {10.1007/BFb0013365},
isbn = {978-3-540-07174-7},
}
@article{FD-FB:13b,
author = {F. D{\"o}rfler and F. Bullo},
journal = {Automatica},
number = {6},
pages = {1539-1564},
title = {Synchronization in Complex Networks of Phase
Oscillators: {A} Survey},
volume = {50},
year = {2014},
abstract = {The emergence of synchronization in a network of
coupled oscillators is a fascinating subject of
multidisciplinary research. This survey reviews the
vast literature on the theory and the applications of
complex oscillator networks. We focus on phase
oscillator models that are widespread in real-world
synchronization phenomena, that generalize the
celebrated Kuramoto model, and that feature a rich
phenomenology. We review the history and the
countless applications of this model throughout
science and engineering. We justify the importance of
the widespread coupled oscillator model as a locally
canonical model and describe some selected
applications relevant to control scientists,
including vehicle coordination, electric power
networks, and clock synchronization. We introduce the
reader to several synchronization notions and
performance estimates. We propose analysis approaches
to phase and frequency synchronization, phase
balancing, pattern formation, and partial
synchronization. We present the sharpest known
results about synchronization in networks of
homogeneous and heterogeneous oscillators, with
complete or sparse interconnection topologies, and in
finite-dimensional and infinite-dimensional settings.
We conclude by summarizing the limitations of
existing analysis methods and by highlighting some
directions for future research.},
doi = {10.1016/j.automatica.2014.04.012},
}
@article{ARB-DJH:81,
author = {A. R. Bergen and D. J. Hill},
journal = {IEEE Transactions on Power Apparatus and Systems},
number = {1},
pages = {25--35},
title = {A structure preserving model for power system
stability analysis},
volume = {100},
year = {1981},
doi = {10.1109/TPAS.1981.316883},
}
@article{TV-AC-EBJ-IC-OS:95,
author = {T. Vicsek and A. Czir\'{o}k and E. Ben-Jacob and
I. Cohen and O. Shochet},
journal = {Physical Review Letters},
number = {6-7},
pages = {1226-1229},
title = {Novel Type of Phase Transition in a System of
Self-Driven Particles},
volume = {75},
year = {1995},
abstract = {A simple model with a novel type of dynamics is
introduced in order to investigate the emergence of
self-ordered motion in systems of particles with
biologically motivated interaction. In our model
particles are driven with a constant absolute
velocity and at each time step assume the average
direction of motion of the particles in their
neighborhood with some random perturbation ( eta )
added. We present numerical evidence that this model
results in a kinetic phase transition from no
transport (zero average velocity, |va| = 0) to finite
net transport through spontaneous symmetry breaking
of the rotational symmetry. The transition is
continuous, since |va| is found to scale as ( eta c-
eta ) beta with beta ~=0.45.},
doi = {10.1103/PhysRevLett.75.1226},
}
@article{NEL-TS-NB-LS-IDC-SAL:12,
author = {N. E. Leonard and T. Shen and B. Nabet and
L. Scardovi and Couzin, I. D. and Levin, S. A.},
journal = {Proceedings of the National Academy of Sciences},
number = {1},
pages = {227--232},
title = {Decision versus compromise for animal groups in
motion},
volume = {109},
year = {2012},
doi = {10.1073/pnas.1118318108},
}
@article{DAP-NEL-RS-DG-JKP:07,
author = {D. A. Paley and N. E. Leonard and R. Sepulchre and
D. Grunbaum and J. K. Parrish},
journal = {{IEEE} Control Systems},
number = {4},
pages = {89-105},
title = {Oscillator Models and Collective Motion},
volume = {27},
year = {2007},
doi = {10.1109/MCS.2007.384123},
}
@article{SL:84,
author = {S. {\L}ojasiewicz},
journal = {Seminari di Geometria 1982-1983},
note = {Istituto di Geometria, Dipartimento di Matematica,
Universit{\`a} di Bologna, Italy},
pages = {115-117},
title = {Sur les trajectoires du gradient d'une fonction
analytique},
year = {1984},
}
@article{PAA-RM-BA:05,
author = {P.-A. Absil and R. Mahony and B. Andrews},
journal = {SIAM Journal on Control and Optimization},
number = {2},
pages = {531--547},
title = {Convergence of the Iterates of Descent Methods for
Analytic Cost Functions},
volume = {6},
year = {2005},
doi = {10.1137/040605266},
}
@article{GG-SK:92,
author = {G. Giorgi and S. Koml{\'o}si},
journal = {Rivista di Matematica Per Le Scienze Economiche e
Sociali},
number = {1},
pages = {3--30},
title = {Dini derivatives in optimization --- {Part I}},
volume = {15},
year = {1992},
doi = {10.1007/BF02086523},
}
@article{JMD:66,
author = {J. M. Danskin},
journal = {SIAM Journal on Applied Mathematics},
number = {4},
pages = {641-664},
title = {The Theory of Max-Min, with Applications},
volume = {14},
year = {1966},
doi = {10.1137/0114053},
}
@book{JLL:1788,
address = {Paris},
author = {Joseph Louis Lagrange},
publisher = {Chez la Veuve Desaint},
title = {M\'ecanique Analytique},
year = {1788},
}
@article{JCM:1868,
author = {J. C. Maxwell},
journal = {Proceedings of the Royal Society. London. Series A.
Mathematical and Physical Sciences},
pages = {270-283},
title = {On Governors},
volume = {16},
year = {1868},
doi = {10.1098/rspl.1867.0055},
}
@book{WT-PGT:1867,
author = {W. Thomson and P. G. Tait},
publisher = {Oxford University Press},
title = {Treatise on Natural Philosophy},
year = {1867},
}
@book{AML:1892,
address = {Kharkov},
author = {Aleksandr Mikhailovich Lyapunov},
note = {Translation:~\citep{AML:1992}},
publisher = {Fakul\cprime{}teta i Khar\cprime{}kovskogo
Matematicheskogo Obshchestva},
title = {Ob\v{s}\v{c}aya zada\v{c}a ob usto\u{\i}\v{c}ivosti
dvi\v{z}eniya},
year = {1892},
}
@article{EAB-NNK:52,
author = {E. A. Barbashin and N. N. Krasovski\u{\i}},
journal = {Doklady Akademii Nauk SSSR},
note = {(In Russian)},
number = {3},
pages = {453-456},
title = {On Global Stability of Motion},
volume = {86},
year = {1952},
}
@book{NNK:63,
author = {N. N. Krasovski\u\i},
publisher = {Stanford University Press},
title = {Stability of Motion. Applications of Lyapunov's
Second Method to Differential Systems and Equations
with Delay},
year = {1963},
}
@article{JPL:60,
author = {J. P. LaSalle},
journal = {IRE Transactions on Circuit Theory},
pages = {520-527},
title = {Some extensions of {L}iapunov's second method},
volume = {CT-7},
year = {1960},
doi = {10.1109/TCT.1960.1086720},
}
@article{JPL:68,
author = {J. P. LaSalle},
journal = {Journal of Differential Equations},
pages = {57--65},
title = {Stability Theory for Ordinary Differential Equations},
volume = {4},
year = {1968},
doi = {10.1016/0022-0396(68)90048-X},
}
@book{JPL:76,
author = {J. P. LaSalle},
publisher = {SIAM},
title = {The Stability of Dynamical Systems},
year = {1976},
doi = {10.1137/1.9781611970432},
isbn = {9780898710229},
}
@book{NGC:61,
author = {Nikolai Gurevich Chetaev},
note = {Translation from Russian by M.~Nadler},
publisher = {Pergamon},
title = {The Stability of Motion},
year = {1961},
}
@book{WH:67,
author = {W. Hahn},
publisher = {Springer},
title = {Stability of Motion},
year = {1967},
isbn = {978-3-642-50085-5},
}
@book{EDS:98,
author = {E. D. Sontag},
edition = {2},
publisher = {Springer},
title = {Mathematical Control Theory: Deterministic Finite
Dimensional Systems},
year = {1998},
isbn = {0387984895},
}
@book{HKK:02,
author = {H. K. Khalil},
edition = {3},
publisher = {Prentice Hall},
title = {Nonlinear Systems},
year = {2002},
isbn = {0130673897},
}
@book{MV:02,
author = {M. Vidyasagar},
publisher = {SIAM},
title = {Nonlinear Systems Analysis},
year = {2002},
doi = {10.1137/1.9780898719185},
isbn = {9780898715262},
}
@book{WMH-SS:74,
author = {M. W. Hirsch and S. Smale},
publisher = {Academic Press},
title = {Differential Equations, Dynamical Systems and Linear
Algebra},
year = {1974},
isbn = {0123495504},
}
@book{VIA:92,
author = {Vladimir I. Arnol'd},
note = {Translation of the third Russian edition by R.~Cooke},
publisher = {Springer},
title = {Ordinary Differential Equations},
year = {1992},
isbn = {3-540-54813-0},
}
@book{JG-PH:90,
author = {J. Guckenheimer and P. Holmes},
publisher = {Springer},
title = {Nonlinear Oscillations, Dynamical Systems, and
Bifurcations of Vector Fields},
year = {1990},
isbn = {0387908196},
}
@book{WMH-VC:08,
author = {W. M. Haddad and V. Chellaboina},
publisher = {Princeton University Press},
title = {Nonlinear Dynamical Systems and Control: A
Lyapunov-Based Approach},
year = {2008},
isbn = {9780691133294},
}
@book{RG-RGS-ART:12,
author = {R. Goebel and R. G. Sanfelice and A. R. Teel},
publisher = {Princeton University Press},
title = {Hybrid Dynamical Systems: Modeling, Stability, and
Robustness},
year = {2012},
isbn = {9780691153896},
}
@book{FB-SM:15,
author = {F. Blanchini and S. Miani},
publisher = {Springer},
title = {Set-Theoretic Methods in Control},
year = {2015},
isbn = {9783319179322},
}
@article{AR:15,
author = {A. Rantzer},
journal = {European Journal of Control},
pages = {72-80},
title = {Scalable control of positive systems},
volume = {24},
year = {2015},
abstract = {Classical control theory does not scale well for
large systems such as power networks, traffic
networks and chemical reaction networks. However,
many such applications in science and engineering can
be efficiently modeled using the concept of positive
systems and the nonlinear counterpart monotone
systems. It is therefore of great interest to see how
such models can be used for control. This paper
demonstrates how positive systems can be exploited
for analysis and design of large-scale control
systems. Methods for synthesis of distributed
controllers are developed based on linear Lyapunov
functions and storage functions instead of quadratic
ones. The main results are extended to frequency
domain input-output models using the notion of
positively dominated system. Applications to
transportation networks and vehicle formations are
provided.},
doi = {10.1016/j.ejcon.2015.04.004},
}
@book{FHC-YSL-RJS-PRW:98,
author = {F. H. Clarke and Y.S. Ledyaev and R. J. Stern and
P. R. Wolenski},
publisher = {Springer},
title = {Nonsmooth Analysis and Control Theory},
year = {1998},
isbn = {0387983368},
}
@article{JC:08-csm,
author = {J. Cort{\'e}s},
journal = {{IEEE} Control Systems},
number = {3},
pages = {36-73},
title = {Discontinuous dynamical systems},
volume = {28},
year = {2008},
abstract = {This paper considers discontinuous dynamical systems,
i.e., systems whose associated vector field is a
discontinuous function of the state. Discontinuous
dynamical systems arise in a large number of
applications, including optimal control, nonsmooth
mechanics, and robotic manipulation. Independently of
the particular application, one always faces similar
questions when dealing with discontinuous dynamical
systems. The most basic one is the notion of
solution. We begin by introducing the notions of
Caratheodory, Filippov and sample-and-hold solutions,
discuss existence and uniqueness results for them,
and examine various examples. We also give specific
pointers to other notions of solution defined in the
literature. Once the notion of solution has been
settled, we turn our attention to the analysis of
stability of discontinuous systems. We introduce the
concepts of generalized gradient of locally Lipschitz
functions and proximal subdifferential of lower
semicontinuous functions. Building on these notions,
we establish monotonic properties of candidate
Lyapunov functions along the solutions. These results
are key in providing suitable generalizations of
Lyapunov stability theorems and the LaSalle
Invariance Principle. We illustrate the applicability
of these results in a class of nonsmooth gradient
flows.},
doi = {10.1109/MCS.2008.919306},
}
@article{RB:62,
author = {R. Bellman},
journal = {Journal of the Society for Industrial and Applied
Mathematics, Series A: Control},
number = {1},
pages = {32--34},
title = {Vector {Lyapunov} functions},
volume = {1},
year = {1962},
doi = {10.1137/0301003},
}
@article{VMS:62,
author = {V. M. Matrosov},
journal = {Journal of Applied Mathematics and Mechanics},
number = {6},
pages = {1506--1522},
title = {On the theory of stability of motion},
volume = {26},
year = {1962},
doi = {10.1016/0021-8928(62)90189-2},
}
@article{JJH:1982,
author = {J. J. Hopfield},
journal = {Proceedings of the National Academy of Sciences},
number = {8},
pages = {2554--2558},
title = {Neural networks and physical systems with emergent
collective computational abilities},
volume = {79},
year = {1982},
abstract = {Computational properties of use of biological
organisms or to the construction of computers can
emerge as collective properties of systems having a
large number of simple equivalent components (or
neurons). The physical meaning of content-addressable
memory is described by an appropriate phase space
flow of the state of a system. A model of such a
system is given, based on aspects of neurobiology but
readily adapted to integrated circuits. The
collective properties of this model produce a
content-addressable memory which correctly yields an
entire memory from any subpart of sufficient size.
The algorithm for the time evolution of the state of
the system is based on asynchronous parallel
processing. Additional emergent collective properties
include some capacity for generalization, familiarity
recognition, categorization, error correction, and
time sequence retention. The collective properties
are only weakly sensitive to details of the modeling
or the failure of individual devices.},
doi = {10.1073/pnas.79.8.2554},
}
@book{SH:08,
author = {S. Haykin},
edition = {3},
publisher = {Prentice Hall},
title = {Neural Networks and Learning Machines},
year = {2008},
isbn = {0131471392},
}
@article{SKP:69,
author = {S. K. Persidskii},
journal = {Avtomat. i Telemekh.},
note = {(Automation and Remote Control, 1970, 30:12,
1889-1895)},
pages = {5--11},
title = {Concerning problem of absolute stability},
volume = {12},
year = {1969},
}
@article{EK-AB:93,
author = {E. Kaszkurewicz and A. Bhaya},
journal = {{SIAM} Journal on Matrix Analysis and Applications},
number = {2},
pages = {508--520},
title = {Robust Stability and Diagonal {Liapunov} Functions},
volume = {14},
year = {1993},
doi = {10.1137/0614036},
}
@book{YT:96,
author = {Y. Takeuchi},
publisher = {World Scientific Publishing},
title = {Global Dynamical Properties of {Lotka-Volterra}
Systems},
year = {1996},
isbn = {9810224710},
}
@unpublished{AJL:82,
author = {A. J. Lohwater},
note = {Unpublished Lecture Notes, reproduced with permission
of Marjorie Lohwater},
title = {{Introduction to Inequalities}},
year = {1982},
url = {http://www.mediafire.com/?1mw1tkgozzu},
}
@unpublished{SB:10,
author = {S. Baigent},
month = mar,
note = {Unpublished Lecture Notes, University of College,
London},
title = {{Lotka-Volterra Dynamics \textemdash{} An
Introduction}},
year = {2010},
annote = {Downloaded on 12/23/2016},
url = {http://www.ltcc.ac.uk/media/london-taught-course-centre/
documents/Bio-Mathematics-(APPLIED).pdf},
}
@article{VV:1926,
author = {V. Volterra},
journal = {Nature},
number = {2983},
pages = {12--13},
title = {Fluctuations in the abundance of a species considered
mathematically},
volume = {119},
year = {1926},
doi = {10.1038/119012b0},
}
@article{BSG:76,
author = {B. S. Goh},
journal = {Journal of Mathematical Biology},
number = {3-4},
pages = {313--318},
title = {Global stability in two species interactions},
volume = {3},
year = {1976},
doi = {10.1007/BF00275063},
}
@article{YT-NA-HT:78,
author = {Y. Takeuchi and N. Adachi and H. Tokumaru},
journal = {Journal of Mathematical Analysis and Applications},
number = {3},
pages = {453--473},
title = {The stability of generalized {Volterra} equations},
volume = {62},
year = {1978},
doi = {10.1016/0022-247X(78)90139-7},
}
@article{BSG:79,
author = {B. S. Goh},
journal = {American Naturalist},
pages = {261--275},
title = {Stability in models of mutualism},
year = {1979},
doi = {10.1086/283384},
}
@book{BSG:80,
author = {B.-S. Goh},
publisher = {Elsevier},
title = {Management and Analysis of Biological Populations},
year = {1980},
isbn = {978-0-444-41793-0},
}
@book{JH-KS:98,
author = {J. Hofbauer and K. Sigmund},
publisher = {Cambridge University Press},
title = {Evolutionary Games and Population Dynamics},
year = {1998},
isbn = {052162570X},
}
@book{WHS:10,
author = {W. H. Sandholm},
publisher = {MIT Press},
title = {Population Games and Evolutionary Dynamics},
year = {2010},
isbn = {0262195879},
}
@article{RP-PM:09,
author = {R. Potrie and P. Monz{\'o}n},
journal = {Dynamical Systems},
number = {1},
pages = {109-115},
title = {Local implications of almost global stability},
volume = {24},
year = {2009},
doi = {10.1080/14689360802474657},
}
@article{FD-FB:10w,
author = {F. D{\"o}rfler and F. Bullo},
journal = {SIAM Journal on Applied Dynamical Systems},
number = {3},
pages = {1070-1099},
title = {On the Critical Coupling for {K}uramoto Oscillators},
volume = {10},
year = {2011},
abstract = {The celebrated Kuramoto model captures various
synchronization phenomena in biological and man-made
dynamical systems of coupled oscillators. It is
well-known that there exists a critical coupling
strength among the oscillators at which a phase
transition from incoherency to synchronization
occurs. This paper features four contributions.
First, we characterize and distinguish the different
notions of synchronization used throughout the
literature and formally introduce the concept of
phase cohesiveness as an analysis tool and
performance index for synchronization. Second, we
review the vast literature providing necessary,
sufficient, implicit, and explicit estimates of the
critical coupling strength in the finite and
infinite-dimensional case and for both first-order
and second-order Kuramoto models. Third, we present
the first explicit necessary and sufficient condition
on the critical coupling strength to achieve
synchronization in the finite-dimensional Kuramoto
model for an arbitrary distribution of the natural
frequencies. The multiplicative gap in the
synchronization condition yields a practical
stability result determining the admissible initial
and the guaranteed ultimate phase cohesiveness as
well as the guaranteed asymptotic magnitude of the
order parameter. As supplementary results, we provide
a statistical comparison of our synchronization
condition with other conditions proposed in the
literature, and we show that our results also hold
for switching and smoothly time-varying natural
frequencies. Fourth and finally, we extend our
analysis to multi-rate Kuramoto models consisting of
second-order Kuramoto oscillators with inertia and
viscous damping together with first-order Kuramoto
oscillators with multiple time constants. We prove
that such a heterogeneous network is locally
topologically conjugate to a first-order Kuramoto
model with scaled natural frequencies. Finally, we
present necessary and sufficient conditions for
almost global phase synchronization and local
frequency synchronization in the multi-rate Kuramoto
model. Interestingly, our provably correct
synchronization conditions do not depend on the
inertiae which contradicts prior observations on the
role of inertial effects in synchronization of
second-order Kuramoto oscillators.},
doi = {10.1137/10081530X},
}
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author = {F. D{\"o}rfler and F. Bullo},
note = {{E}xtended version including proofs.},
title = {Exploring Synchronization in Complex Oscillator
Networks},
year = {2012},
url = {http://arxiv.org/pdf/1209.1335},
}
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address = {Paris, France},
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author = {Y. Kuramoto},
publisher = {Springer},
title = {Chemical Oscillations, Waves, and Turbulence},
year = {1984},
isbn = {0387133224},
}
@article{SHS:00,
author = {S. H. Strogatz},
journal = {Physica D: Nonlinear Phenomena},
number = {1},
pages = {1-20},
title = {From {Kuramoto} to {C}rawford: {E}xploring the onset
of synchronization in populations of coupled
oscillators},
volume = {143},
year = {2000},
abstract = {The Kuramoto model describes a large population of
coupled limit-cycle oscillators whose natural
frequencies are drawn from some prescribed
distribution. If the coupling strength exceeds a
certain threshold, the system exhibits a phase
transition: some of the oscillators spontaneously
synchronize, while others remain incoherent. The
mathematical analysis of this bifurcation has proved
both problematic and fascinating. We review 25 years
of research on the Kuramoto model, highlighting the
false turns as well as the successes, but mainly
following the trail leading from Kuramoto’s work to
Crawford’s recent contributions. It is a lovely
winding road, with excursions through mathematical
biology, statistical physics, kinetic theory,
bifurcation theory, and plasma physics.},
doi = {10.1016/S0167-2789(00)00094-4},
}
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{A} new hypothesis},
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doi = {10.1161/01.RES.61.5.704},
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Martinerie, J.},
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year = {2001},
doi = {10.1038/35067550},
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Celebratory Volume in Honor of Larry Sirovich},
editor = {E. Kaplan and J. E. Marsden and K. R. Sreenivasan},
pages = {183--215},
publisher = {Springer},
title = {Globally coupled oscillator networks},
year = {2003},
doi = {10.1007/978-0-387-21789-5_5},
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networks of coupled cortical oscillators},
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year = {1997},
doi = {10.1023/A:1008843412952},
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}
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Coolen, A. C. C. and Perez-Vicente, C.},
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author = {Kiss, I. Z. and Zhai, Y. and Hudson, J. L.},
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year = {2002},
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@article{PAT:03,
author = {P. A. Tass},
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title = {A model of desynchronizing deep brain stimulation
with a demand-controlled coordinated reset of neural
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year = {2003},
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}
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journal = {IEEE Transactions on Automatic Control},
number = {5},
pages = {811-824},
title = {Stabilization of Planar Collective Motion:
{A}ll-to-all Communication},
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year = {2007},
doi = {10.1109/TAC.2007.898077},
}
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number = {4},
pages = {695--705},
title = {Integration of communication and control using
discrete time {Kuramoto} models for multivehicle
coordination over broadcast networks},
volume = {26},
year = {2008},
doi = {10.1109/JSAC.2008.080511},
}
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}
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memory, and optical neurocomputing},
volume = {62},
year = {2000},
doi = {10.1103/PhysRevE.62.4010},
}
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author = {R. A. York and R. C. Compton},
journal = {IEEE Transactions on Microwave Theory and Techniques},
number = {6},
pages = {1000--1009},
title = {Quasi-optical power combining using mutually
synchronized oscillator arrays},
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year = {1991},
doi = {10.1109/22.81670},
}
@article{JWSP-FD-FB:12u,
author = {J. W. Simpson-Porco and F. D{\"o}rfler and F. Bullo},
journal = {Automatica},
number = {9},
pages = {2603-2611},
title = {Synchronization and Power Sharing for
Droop-Controlled Inverters in Islanded Microgrids},
volume = {49},
year = {2013},
abstract = {Motivated by the recent and growing interest in smart
grid technology, we study the operation of DC/AC
inverters in a lossless microgrid. We show that a
network of loads and DC/AC inverters equipped with
power-frequency droop controllers can be cast as a
Kuramoto model of phase-coupled oscillators. This
novel description, together with results from the
theory of coupled oscillators, allows us to
characterize the behavior of the network of inverters
and loads. Specifically, we provide a necessary and
sufficient condition for the existence of a
synchronized solution that is unique and locally
exponentially stable. We present a selection of
controller gains leading to a desirable sharing of
power among the inverters, and specify the set of
loads which can be serviced without violating given
actuation constraints. Moreover, we propose a
distributed integral controller based on averaging
algorithms, which dynamically regulates the system
frequency in the presence of a time-varying load.
Remarkably, this distributed-averaging integral
controller has the additional property that it
preserves the power sharing properties of the primary
droop controller. Our results hold without
assumptions on identical line characteristics or
voltage magnitudes.},
doi = {10.1016/j.automatica.2013.05.018},
}
@article{JAA-LLB-CJPV-FR-RS:05,
author = {J. A. Acebr{\'o}n and L. L. Bonilla and
C. J. P. Vicente and F. Ritort and R. Spigler},
journal = {Reviews of Modern Physics},
number = {1},
pages = {137--185},
title = {The {Kuramoto} model: {A} simple paradigm for
synchronization phenomena},
volume = {77},
year = {2005},
abstract = {Synchronization phenomena in large populations of
interacting elements are the subject of intense
research efforts in physical, biological, chemical,
and social systems. A successful approach to the
problem of synchronization consists of modeling each
member of the population as a phase oscillator. In
this review, synchronization is analyzed in one of
the most representative models of coupled phase
oscillators, the Kuramoto model. A rigorous
mathematical treatment, specific numerical methods,
and many variations and extensions of the original
model that have appeared in the last few years are
presented. Relevant applications of the model in
different contexts are also included.},
doi = {10.1103/RevModPhys.77.137},
}
@article{AA-ADG-JK-YM-CZ:08,
author = {A. Arenas and A. D{\'\i}az-Guilera and J. Kurths and
Y. Moreno and C. Zhou},
journal = {Physics Reports},
number = {3},
pages = {93--153},
title = {Synchronization in complex networks},
volume = {469},
year = {2008},
abstract = {Synchronization processes in populations of locally
interacting elements are the focus of intense
research in physical, biological, chemical,
technological and social systems. The many efforts
devoted to understanding synchronization phenomena in
natural systems now take advantage of the recent
theory of complex networks. In this review, we report
the advances in the comprehension of synchronization
phenomena when oscillating elements are constrained
to interact in a complex network topology. We also
take an overview of the new emergent features coming
out from the interplay between the structure and the
function of the underlying patterns of connections.
Extensive numerical work as well as analytical
approaches to the problem are presented. Finally, we
review several applications of synchronization in
complex networks to different disciplines: biological
systems and neuroscience, engineering and computer
science, and economy and social sciences.},
doi = {10.1016/j.physrep.2008.09.002},
}
@inproceedings{AM-PS-RJS:12,
address = {Maui, HI, USA},
author = {A. Mauroy and P. Sacr{\'e} and R. J. Sepulchre},
booktitle = {{IEEE} Conf.\ on Decision and Control},
month = dec,
pages = {7171-7183},
title = {Kick Synchronization versus Diffusive
Synchronization},
year = {2012},
doi = {10.1109/CDC.2012.6425821},
}
@article{AG-EM-AT:16,
author = {A. Gushchin and E. Mallada and A. Tang},
journal = {IEEE Transactions on Network Science and Engineering},
number = {4},
pages = {240-256},
title = {Phase-Coupled Oscillators with Plastic Coupling:
Synchronization and Stability},
volume = {3},
year = {2016},
doi = {10.1109/TNSE.2016.2605096},
}
@inproceedings{GT-MM:23,
author = {G. Tong and M. Muehlebach},
booktitle = {Learning for Dynamics and Control Conference},
organization = {PMLR},
pages = {1373--1386},
title = {A Dynamical Systems Perspective on Discrete
Optimization},
year = {2023},
}
@incollection{TW-JR:19,
author = {T. Wang and J. Roychowdhury},
booktitle = {Unconventional Computation and Natural Computation},
pages = {232--256},
publisher = {Springer},
title = {{OIM}: Oscillator-Based {Ising} Machines for Solving
Combinatorial Optimisation Problems},
year = {2019},
doi = {10.1007/978-3-030-19311-9_19},
}
@book{AML:1992,
author = {Aleksandr Mikhailovich Lyapunov},
note = {Translation from Russian by A.~T.~Fuller},
publisher = {Taylor \& Francis},
title = {The General Problem of the Stability of Motion},
year = {1992},
}