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

Department of Engineering Mathematics, University of Bristol, BS8 1TR,Bristol, U.K. {m.dibernardo@bristol.ac.uk}AbstractIn this paper we extend to a generic class of piecewise smooth dynamical systems afundamental tool for the analysis of convergence of smooth dynamical systems: con-traction theory. We focus on switched systems satisfying Caratheodory conditionsfor the existence and unicity of a solution. After generalizing the classical definitionof contraction to this class of dynamical systems, we give sufficient conditions forglobal exponential convergence of their trajectories. The theoretical results are thenapplied to solve a set of representative problems including proving global asymp-totic stability of switched linear systems, giving conditions for incremental stabilityof piecewise smooth systems, and analyzing the convergence of networked switchedlinear systems.

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