Contraction analysis of switched systems: the case of Caratheodory Systems and Networks

TL;DR

This paper extends contraction theory to a broad class of piecewise smooth switched systems satisfying Caratheodory conditions, providing conditions for their global exponential convergence and stability analysis.

Contribution

It generalizes contraction analysis to Caratheodory systems and offers new criteria for stability and convergence of switched and networked systems.

Findings

Established sufficient conditions for global exponential convergence.

Proved global asymptotic stability of switched linear systems.

Analyzed convergence in networked switched systems.

Abstract

In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched systems satisfying Caratheodory conditions for the existence and unicity of a solution. After generalizing the classical definition of contraction to this class of dynamical systems, we give sufficient conditions for global exponential convergence of their trajectories. The theoretical results are then applied to solve a set of representative problems including proving global asymptotic stability of switched linear systems, giving conditions for incremental stability of piecewise smooth systems, and analyzing the convergence of networked switched linear systems.