Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems

Philippe Jouan (1) , Said Naciri (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated by many examples.

Mots clés: Switched systems; Asymptotic stability; Weak Lyapunov functions; Chaotic signals; Omega-limit sets

Domaines: Optimisation et contrôle [math.OC]

Philippe Jouan, Said Naciri. Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems. 2012. ⟨hal-00745780⟩