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Publications about 'Contraction Theory'

Books and proceedings

  1. F. Bullo. Contraction Theory for Dynamical Systems. Kindle Direct Publishing, 1.3 edition, 2026. PDF [bibtex-entry]

Thesis

  1. S. Betteti. Associative Memory and Recurrent Neural Networks: A Dynamical Systems Approach. PhD thesis, Information Engineering Department, Universitŕ di Padova, Italy, February 2026. PDF Keyword(s): Contraction Theory, Network Systems, Machine Learning, Neural Networks, Theoretical Neuroscience. [bibtex-entry]
  2. A. Davydov. Contraction Theory in Control, Learning, and Optimization. PhD thesis, Mechanical Engineering Department, University of California at Santa Barbara, June 2025. PDF Keyword(s): Contraction Theory, Network Systems, Machine Learning, Neural Networks. [bibtex-entry]
  3. V. Centorrino. Contracting Dynamics for Biologically Plausible Neural Networks and Optimization. PhD thesis, Modeling and Engineering Risk and Complexity, Scuola Superiore Meridionale, December 2024. PDF Keyword(s): Contraction Theory, Network Systems, Machine Learning, Neural Networks, Theoretical Neuroscience. [bibtex-entry]
  4. S. Jaffe. Dynamical Systems and Neural Networks: From Implicit Models to Memory Retrieval. PhD thesis, Computer Science Department, University of California at Santa Barbara, September 2024. PDF Keyword(s): Contraction Theory, Network Systems, Machine Learning. [bibtex-entry]
  5. F. Seccamonte. Bilevel Optimization in Learning and Control with Applications to Network Flow Estimation. PhD thesis, Mechanical Engineering Department, University of California at Santa Barbara, September 2023. PDF Keyword(s): Contraction Theory, Network Systems, Power Networks. [bibtex-entry]
  6. K. D. Smith. Control and Estimation in Network Systems. PhD thesis, Electrical and Computer Engineering Department, University of California at Santa Barbara, December 2022. PDF Keyword(s): Contraction Theory, Network Systems, Power Networks. [bibtex-entry]
  7. P. Cisneros-Velarde. Network systems: Social networks, Epidemics, Optimization and Contraction Theory. PhD thesis, Mechanical Engineering Department, University of California at Santa Barbara, July 2021. PDF Keyword(s): Social Networks, Contraction Theory, Network Systems. [bibtex-entry]

Articles in journal or book chapters

  1. K. Boonyawat and F. Bullo. On Proportional-Integral Control of Contracting Dynamics. IEEE Transactions on Automatic Control, 2026. Note: Submitted. Keyword(s): Contraction Theory. [bibtex-entry]
  2. Y. Chen, F. Bullo, and E. Dall'Anese. Sampled-data Systems: Stability, Contractivity and Single-iteration Suboptimal MPC. IEEE Transactions on Automatic Control, 2026. Note: To appear. Keyword(s): Nonlinear Control, Contraction Theory. [bibtex-entry]
  3. L. Cothren, F. Bullo, and E. Dall'Anese. Online Feedback Optimization and Singular Perturbation via Contraction Theory. SIAM Journal on Control and Optimization, 64(3):1482--1506, 2026. Keyword(s): Contraction Theory. [bibtex-entry]
  4. A. Gokhale, A. V. Proskurnikov, Y. Kawano, and F. Bullo. A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning. IEEE Transactions on Automatic Control, April 2026. Note: Submitted. [bibtex-entry]
  5. Y. Kawano, S. Betteti, A. Davydov, and F. Bullo. Incremental input-to-state stability and equilibrium tracking for stochastic contracting dynamics. IEEE Transactions on Automatic Control, 2026. Note: Submitted. Keyword(s): Contraction Theory. [bibtex-entry]
  6. Y. Kawano and F. Bullo. Contractivity of Multi-Stage Runge--Kutta Dynamics. Automatica, 2026. Note: Submitted. Keyword(s): Contraction Theory. [bibtex-entry]
  7. Y. Kawano and F. Bullo. Input-to-State Stability Implications in Contraction Theory. Automatica, 2026. Note: Submitted. Keyword(s): Contraction Theory. [bibtex-entry]
  8. Z. Marvi, F. Bullo, and A. G. Alleyne. Air Cooled Battery Pack Thermal Management via Control Barrier Proximal Dynamics. IEEE Transactions on Control Systems Technology, 2026. Note: To appear. Keyword(s): Contraction Theory. [bibtex-entry]
  9. R. Ofir, F. Bullo, and M. Margaliot. A Sufficient Condition for 2-Contraction of a Feedback Interconnection. IEEE Transactions on Automatic Control, 71(2):1207-1214, 2026. Keyword(s): Contraction Theory. [bibtex-entry]
  10. A. V. Proskurnikov and F. Bullo. Regular Pairings for Non-Quadratic Lyapunov Functions and Contraction Analysis. SIAM Journal on Control and Optimization, 64(1):496-521, 2026. Keyword(s): Contraction Theory. [bibtex-entry]
  11. S. Betteti and F. Bullo. Contraction and Concentration of Measures with Applications to Theoretical Neuroscience. Automatica, April 2025. Note: Submitted. Keyword(s): Contraction Theory, Theoretical Neuroscience. [bibtex-entry]
  12. A. Davydov, V. Centorrino, A. Gokhale, G. Russo, and F. Bullo. Time-Varying Convex Optimization: A Contraction and Equilibrium Tracking Approach. IEEE Transactions on Automatic Control, 70(11):7446-7460, 2025. Keyword(s): Contraction Theory. [bibtex-entry]
  13. A. Davydov, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Contraction Analysis of Continuous-Time Neural Networks. IEEE Transactions on Automatic Control, 70(1):235-250, 2025. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  14. Z. Marvi, F. Bullo, and A. G. Alleyne. Discrete Control Barrier Proximal Dynamics: Quantized Multi-Actuator and Sampled-data Systems. Automatica, 2025. Note: To appear. Keyword(s): Contraction Theory. [bibtex-entry]
  15. V. Centorrino, F. Bullo, and G. Russo. Modelling and Contractivity of Neural-Synaptic Networks with Hebbian Learning. Automatica, 164:111636, 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  16. V. Centorrino, A. Davydov, A. Gokhale, G. Russo, and F. Bullo. On Weakly Contracting Dynamics for Convex Optimization. IEEE Control Systems Letters, 8:1745-1750, 2024. Keyword(s): Contraction Theory. [bibtex-entry]
  17. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Positive Competitive Networks for Sparse Reconstruction. Neural Computation, 36(6):1163–1197, 2024. Keyword(s): Contraction Theory, Neural Networks, Theoretical Neuroscience. [bibtex-entry]
  18. O. Dalin, R. Ofir, E. Bar Shalom, A. Ovseevich, F. Bullo, and M. Margaliot. Verifying $k$-Contraction without Computing $k$-Compounds. IEEE Transactions on Automatic Control, 69(3):1492-1506, 2024. Keyword(s): Contraction Theory. [bibtex-entry]
  19. A. Davydov and F. Bullo. Exponential Stability of Parametric Optimization-Based Controllers via Lur'e contractivity. IEEE Control Systems Letters, 8:1277-1282, 2024. Keyword(s): Contraction Theory. [bibtex-entry]
  20. A. Davydov and F. Bullo. Perspectives on Contractivity in Control, Optimization and Learning. IEEE Control Systems Letters, 8:2087-2098, 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  21. A. Davydov, S. Jafarpour, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Monotone Operator Theory and Applications. Journal of Machine Learning Research, 25(307):1-33, 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  22. G. De Pasquale, K. D. Smith, F. Bullo, and M. E. Valcher. Dual Seminorms, Ergodic Coefficients, and Semicontraction Theory. IEEE Transactions on Automatic Control, 69(5):3040-3053, 2024. Keyword(s): Contraction Theory. [bibtex-entry]
  23. A. Gokhale, A. Davydov, and F. Bullo. Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications. IEEE Control Systems Letters, 8:2853-2858, 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  24. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Euclidean Contractivity of Neural Networks with Symmetric Weights. IEEE Control Systems Letters, 7:1724-1729, 2023. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  25. R. Delabays and F. Bullo. Semicontraction and Synchronization of Kuramoto-Sakaguchi Oscillator Networks. IEEE Control Systems Letters, 7:1566-1571, 2023. Keyword(s): Contraction Theory, Oscillator Networks. [bibtex-entry]
  26. S. Jafarpour, A. Davydov, and F. Bullo. Non-Euclidean Contraction Theory for Monotone and Positive Systems. IEEE Transactions on Automatic Control, 68(9):5653-5660, 2023. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  27. A. V. Proskurnikov, A. Davydov, and F. Bullo. The Yakubovich S-Lemma Revisited: Stability and Contractivity in Non-Euclidean Norms. SIAM Journal on Control and Optimization, 61(4):1955-1978, 2023. Keyword(s): Contraction Theory. [bibtex-entry]
  28. K. D. Smith and F. Bullo. Contractivity of the Method of Successive Approximations for Optimal Control. IEEE Control Systems Letters, 7:919-924, 2023. Keyword(s): Contraction Theory. [bibtex-entry]
  29. P. Cisneros-Velarde, S. Jafarpour, and F. Bullo. A Contraction Analysis of Primal-Dual Dynamics in Distributed and Time-Varying Implementations. IEEE Transactions on Automatic Control, 67(7):3560-3566, 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  30. P. Cisneros-Velarde, S. Jafarpour, and F. Bullo. Contraction Theory for Dynamical Systems on Hilbert Spaces. IEEE Transactions on Automatic Control, 67(12):6710-6715, 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  31. A. Davydov, S. Jafarpour, and F. Bullo. Non-Euclidean Contraction Theory for Robust Nonlinear Stability. IEEE Transactions on Automatic Control, 67(12):6667-6681, 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  32. S. Jafarpour, P. Cisneros-Velarde, and F. Bullo. Weak and Semi-Contraction for Network Systems and Diffusively-Coupled Oscillators. IEEE Transactions on Automatic Control, 67(3):1285-1300, 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  33. R. Ofir, F. Bullo, and M. Margaliot. Minimum Effort Decentralized Control Design for Contracting Network Systems. IEEE Control Systems Letters, 6:2731-2736, 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  34. J. W. Simpson-Porco and F. Bullo. Contraction Theory on Riemannian Manifolds. Systems & Control Letters, 65:74-80, 2014. PDF Keyword(s): Nonlinear Control, Mechanical Control Systems, Contraction Theory. [bibtex-entry]

Conference articles

  1. F. Bullo, S. Coogan, E. Dall'Anese, I. R. Manchester, and G. Russo. Advances in Contraction Theory for Robust Optimization, Control, and Neural Computation. In IEEE Conf. on Decision and Control, Rio de Janeiro, Brazil, 2025. [bibtex-entry]
  2. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Biologically Plausible Neural Networks for Sparse Reconstruction: A Normative Framework. In Workshop “Mathematics for Artificial Intelligence and Machine Learning”, Milan, Italy, january 2024. Note: Oral Presentation. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  3. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Towards a Top/Down Normative Framework for a Biologically Plausible Explanation of Neural Circuits: Application to Sparse Reconstruction Problems. In 5th International Convention on the Mathematics of Neuroscience and AI, Rome, Italy, May 2024. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  4. V. Centorrino, A. Gokhale, A. Davydov, G. Russo, and F. Bullo. Contractivity of Symmetric Neural Networks for Non-negative Sparse Approximation. In CCS/Italy 2023 Italian Regional Conference on Complex Systems, Naples, Italy, october 2023. Note: Poster Presentation. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  5. V. Centorrino, F. Bullo, and G. Russo. Contraction Analysis of Hopfield Neural Networks with Hebbian Learning. In IEEE Conf. on Decision and Control, Cancun, Mexico, December 2022. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  6. P. Cisneros-Velarde and F. Bullo. A Contraction Theory Approach to Optimization Algorithms from Acceleration Flows. In International Conference on Artificial Intelligence and Statistics, May 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  7. A. Davydov, S. Jafarpour, M. Abate, F. Bullo, and S. Coogan. Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks. In IEEE Conf. on Decision and Control, Cancun, Mexico, 2022. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  8. A. Davydov, S. Jafarpour, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks. In IEEE Conf. on Decision and Control, Cancun, Mexico, December 2022. Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  9. A. Davydov, A. V. Proskurnikov, and F. Bullo. Non-Euclidean Contractivity of Recurrent Neural Networks. In American Control Conference, Atlanta, USA, pages 1527-1534, May 2022. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  10. S. Jafarpour, M. Abate, A. Davydov, F. Bullo, and S. Coogan. Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach. In Learning for Dynamics and Control Conference, June 2022. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]
  11. S. Jafarpour, A. Davydov, M. Abate, F. Bullo, and S. Coogan. Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach. In ICML Workshop on Formal Verification of Machine Learning, July 2022. Keyword(s): Contraction Theory. [bibtex-entry]
  12. K. D. Smith, F. Seccamonte, A. Swami, and F. Bullo. Physics-Informed Implicit Representations of Equilibrium Network Flows. In Advances in Neural Information Processing Systems, November 2022. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  13. F. Bullo, P. Cisneros-Velarde, A. Davydov, and S. Jafarpour. From Contraction Theory to Fixed Point Algorithms on Riemannian and non-Euclidean Spaces. In IEEE Conf. on Decision and Control, December 2021. PDF Keyword(s): Contraction Theory. [bibtex-entry]
  14. S. Jafarpour, A. Davydov, A. V. Proskurnikov, and F. Bullo. Robust Implicit Networks via Non-Euclidean Contractions. In Advances in Neural Information Processing Systems, volume 34, pages 9857--9868, December 2021. PDF Keyword(s): Contraction Theory, Neural Networks. [bibtex-entry]

Miscellaneous

  1. G. De Pasquale, K. D. Smith, F. Bullo, and M. E. Valcher. Dual Seminorms, Ergodic Coefficients, and Semicontraction Theory, 2022. Note: Available at http://arxiv.org/abs/2201.03103. Keyword(s): Contraction Theory. [bibtex-entry]
  2. S. Jafarpour, P. Cisneros-Velarde, and F. Bullo. Weak and Semi-Contraction Theory with Application to Network Systems, 2020. Note: ArXiv e-print. PDF Keyword(s): Contraction Theory. [bibtex-entry]

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