Stability and L2 gain analysis for a class of switched symmetric systems

In this paper, we study stability and L-2 gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric subsystems. We focus our attention mainly on discrete-time systems. When all subsystems are Schur stable, we show that the switched system is exponentially stable under arbitrary switching. Furthermore, we show that when all subsystems are Schur stable and have L-2 gains smaller than a positive scalar gamma, the switched system is exponentially stable and has an L-2 gain smaller than the same gamma under arbitrary switching. The key idea for both stability and L-2 gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.