A Note on Multiple Lyapunov Functions and Stability Condition for Switched and Hybrid Systems

Abstract

In this note, we consider stability condition with multiple Lyapunov for switched and hybrid systems. By using idea of evaluating the average value of multiple Lyapunov functions during activation period of each subsystem, we propose a new Lyapunov stability condition, which complements existing stability conditions that evaluate value of multiple Lyapunov at starting points or end points. We present several demonstrative examples, including case where unstable subsystems are involved, and also apply stability condition and switching strategy to switching control problem for stabilization of nonholonomic systems.