In this paper, we study stability and /spl Lscr//sub 2/ gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric sub-systems. 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 /spl Lscr//sub 2/ gains smaller than a positive scalar /spl gamma/, the switched system is exponentially stable and has an /spl Lscr//sub 2/ gain smaller than the same /spl gamma/ under arbitrary switching. The key idea for both stability and /spl Lscr//sub 2/ gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.