Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

TLDR

The paper focuses on stability analysis of switched and hybrid systems. The study introduces analysis tools for switched and hybrid systems and extends Bendixson's theorem to enable limit cycle analysis of continuous switched systems. The authors employ multiple Lyapunov functions and iterated function system theory, and consider systems indexed by arbitrary compact sets, to analyze Lyapunov and Lagrange stability.

Abstract

We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.