LAUSR

This paper investigates the stability for a class of discrete-time switched $$\Phi $$Φ-systems without assuming the stability for any subsystem. Based on the single Lyapunov function method and the multiple Lyapunov functions method, respectively, switching laws depending on the system state are designed, which can guarantee the stability of the switched system. In particular, when the proposed single Lyapunov function method is used, the stability of the convex combination of the system matrices is not required, which extends the classic single Lyapunov method. Two examples illustrate the effectiveness of the results.