Input-to-state stability of switched systems with time delays

Abstract

This chapter deals with the input-to-state stability of switched nonlinear systems with time delays. The proposed results demonstrate a connection between small-gain arguments in the context of input-to-state stability and the traditional Lyapunov-Razumikhin method for switched systems. By using the notion of average dwell time, it is shown that a switching among ISS systems with compatible Lyapunov-Razumikhin functions will not destroy the stability property if the switching is not too fast on average. Particularly, it is shown that the existence of a common Razumikhin function is sufficient to guarantee input-to-state stability for time-delayed systems under arbitrary switching.