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

1998/04/01 by M.S. Branicky, Michael S. Branicky · 42 citations
Engineering · Mathematics · #Stability and Control of Uncertain Systems #Control and Stability of Dynamical Systems #Advanced Differential Equations and Dynamical Systems

paper · doi:10.1109/9.664150

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.

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