In this work we consider the input-to-state stability property for a switched system containing both delayed input-to-state stable subsystems and delayed unstable (but forward complete) subsystems. Our main approach is based on the Lyapunov-Razumikhin functions. By using the notion of average dwell time, it is demonstrated that for a system switching among subsystems that admit comparable Lyapunov-Razumikhin type of functions, if a switching signal is not switching too fast and if the activation time of unstable subsystems is not too long, then the resulted switched system is ISS.
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