Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems

TL;DR

This paper investigates the asymptotic stability of nonlinear switched systems using common weak Lyapunov functions, extending linear system results to broader classes of inputs and providing geometric stability conditions.

Contribution

It introduces new stability conditions for nonlinear switched systems under nonchaotic inputs, generalizing previous linear system results with geometric criteria.

Findings

Sufficient conditions for asymptotic stability are established.

Results extend linear system stability to nonlinear cases.

Numerous examples illustrate the theoretical findings.

Abstract

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.