Abstract: The problem of stability with H∞ performance for a class of linear discrete-time switched systems is discussed under the action of arbitrary switching. The system taken into consideration consists of several linear discrete-time subsystems of which each is stable with H∞ performance. It is well known that the switched system may be unstable under some switching actions between asymptotically stable subsystems, so it is not certainly stable with H∞ performance under the action of any switching. Based on the known bounded real lemma, a sufficient condition for the solvability of the problem is given in terms of linear matrix inequalities (LMIs) by using common Lyapunov function method. A simulation of a practical example is conducted to show the effectiveness of the result.