Contraction Theory for Dynamical Systems

CTDS 

Francesco Bullo

Department of Mechanical Engineering
Center for Control, Dynamical-Systems, and Computation
University of California, Santa Barbara
bullo at ucsb.edu

Edition 1.2, Aug 1, 2024
252 pages and 94 exercises
Kindle Direct Publishing
ISBN 979-8836646806

Abstract

These lecture notes provide a mathematical introduction to contraction theory for dynamical systems. Special emphasis is given to continuous-time differential equations arising in the study of network multi-agent systems, monotone dynamics, and semi-contracting systems. This document is version 1.2 on August 1, 2024.

These notes cover (i) the manifold properties of the induced norms and logarithmic norms of matrices, (ii) contracting dynamics over finite-dimensional vector spaces endowed with Euclidean and non-Euclidean norms, (iii) weakly-contracting dynamics and monotone dynamics, and (iv) semicontracting, perpendicularly and partially contracting systems. Numerous examples are presented in some detail, including Hopfield neural networks, systems in Lure’ form, interconnected contracting systems, gradient and primal dual flows of convex functions, Lotka-Volterra population dynamics, Daganzo traffic models, averaging flows, and diffusively-coupled synchronizing systems.

Book versions and purchase/download information

The book may be purchased or downloaded in the following versions:

Solution manual
I repeat: the solution manual is freely available upon request ONLY for instructors at accredited institutions. If you are not an instructor at an accredited institution, please do not email me in the hope of receiving a copy.

Additionally, the following documents are downloadable:

Citation information
@Book{FB-CTDS,
  author =    {F. Bullo},
  title =     {Contraction Theory for Dynamical Systems},
  year =      2024,
  edition =   {{1.2}},
  publisher = {Kindle Direct Publishing},
  ISBN =      {979-8836646806},
  url =       {https://fbullo.github.io/ctds},
}

Tutorial slides and Youtube lectures

Copyright information

This book is intended for personal non-commercial use only: you may not use this material for commercial purposes and you may not copy and redistribute this material in any medium or format.

Why I decided to self-publish a print-on-demand book

There are several reasons why I decided to self-publish this book via the print-on-demand service by Kindle Direct Publishing (former Amazon CreateSpace). I appreciate the ability to:

As a combination of this flexibility, I typically polish and enrich the book every time I teach the course.

Similar arguments are presented in the write-up Why I Self-Publish My Mathematics Texts With Amazon by Robert Ghrist

History

Feedback

I am thankful for any feedback information, including suggestions, evaluations, error descriptions, or comments about teaching or research uses. Please email bullo at ucsb.edu