P.-A. Bliman and G. Ferrari-Trecate. Stability analysis of discrete-time switched systems through lyapunov functions with nonminimal state. IFAC Conference on the Analysis and Design of Hybrid Systems (ADHS 03) , 2003. St. Malo, France, 16-18 June.
In this paper we investigate stability analysis for discrete-time switched systems. We first consider quadratic Lyapunov functionsdefined over a nonminimal state encompassing the past history ofthe state trajectory over a finite horizon. This allows us tostate necessary and sufficient conditions for testing uniformexponential stability. Quite remarkably, such conditions can berecast into suitable Linear Matrix Inequalities (LMIs). Next, weconsider more general Lyapunov functions dependent also on thepast of the switch trajectory. We show that, despite the increasedflexibility, this class is no more powerful in capturing stabilitythan the previous class of quadratic Lyapunov functions. However, the associatedLMI-based tests may be computationally more advantageous than theones derived in the quadratic case.