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

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