Contraction analysis for a class of nondifferentiable systems with applications to stability and network synchronization

Mario Di Bernardo, Davide Liuzza, Giovanni Russo

Research output: Contribution to journalArticle (Academic Journal)peer-review

25 Citations (Scopus)

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 nondifferentiable systems satisfying Carathéodory conditions for the existence and uniqueness of a solution. After generalizing the classical definition of contraction to this class of dynamical systems, we give sufficient conditions for global convergence of their trajectories. The theoretical results are then applied to solve a set of representative problems such as proving global asymptotic stability of switched linear systems, giving conditions for incremental stability of piecewise smooth systems, and analyzing the convergence of networked switched systems.

Original languageEnglish
Pages (from-to)3203-3227
Number of pages25
JournalSIAM Journal on Control and Optimization
Volume52
Issue number5
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Contraction theory
  • Convergence
  • Networks
  • Piecewise smooth systems

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