Global exponential stability of switched systems

Abstract

This paper proposes a method for the stability analysis of deterministic switched systems. Two motivational examples are introduced (nonholonomic system and constrained pendulum). The finite collection of models consists of nonlinear models, and a switching sequence is arbitrary. It is supposed that there is no jump in the state at switching instants, and there is no Zeno behavior, i.e., there is a finite number of switches on every bounded interval. For the analysis of deterministic switched systems, the multiple Lyapunov functions are used, and the global exponential stability is proved. The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations. © 2011 Shanghai University and Springer-Verlag Berlin Heidelberg.