A NOTE ON MULTIPLE LYAPUNOV FUNCTIONS AND STABILITY CONDITION FOR SWITCHED AND HYBRID SYSTEMS

作者：Zhai Guisheng^*; Matsune Isatada; Imae Joe; Kobayashi Tomoaki

来源：International Journal of Innovative Computing Information and Control, 2009, 5(5): 1189-1199.

• Switched and hybrid systems
• Multiple Lyapunov functions
• Lyapunov stability
• Switching strategy
• Average value of multiple Lyapunov functions
• Nonholonomic systems

In this note, we consider stability condition with multiple Lyapunov junctions for switched and hybrid systems. By using the idea of evaluating "the average value of multiple Lyapunov functions" during the activation interval 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 ending 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.

• 出版日期2009-5