This paper is concerned with the problem of fault detection and isolation (FDI) for discrete-time switched systems under an arbitrary switching signal. A family of fault detection and isolation filters is designed. In virtue of the frequency of the faults in a given range, the finite-frequency 𝐻− performance for the switched system is firstly defined. Based on a switched Lyapunov functional approach, a procedure of FDI filters synthesis is established by Linear matrix inequalities (LMIs), and the filter gains are characterized in terms of the solution of a convex optimization problem. A numerical example is used to demonstrate the effectiveness of the proposed design method.