The problem of H∞ filtering for a class of discrete-time switched systems with delays is considered. When all the
subsystems are stable, a sufficient condition for the asymptotic stability with the prescribed H∞ performance gamma of filtering
error systems is obtained based on switched Lyapunov function technique and Finsler lemma. Though each subsystem of
the switched system is not stable, a stable switched system can be guaranteed by utilizing multiple Lyapunov functions
method and state-dependent switching technique. Then, a desired H∞ filter can be designed and a sufficient condition with
prescribed H∞ performance gamma of filtering error systems is obtained. Finally, a numerical example is provided to demonstrate
the effectiveness of the proposed design method.