Contraction Theory for Dynamical Systems

By Francesco Bullo

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.

• Format: Paperback
• Language: English
• ISBN: B0B4K1BTF4
• ISBN13: 9798836646806
• Release Date: June 2022
• Publisher: Independently published
• Length: 252 Pages
• Dimensions: 10.0" x 0.6" x 7.0"