Robust Stability and Stabilization of Switched Systems with Dwell Time

Abstract

Sufficient conditions for the stability of linear-switched systems with dwell-time and polytopic-type parameter uncertainties are presented. A Lyapunov function, in quadratic form, which is nonincreasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs and it becomes time invariant afterward. This function leads to asymptotic stability conditions for the nominal set of the subsystems that can be readily extended to the case where these subsystems suffer from polytopic-type parameter uncertainties. The method proposed is then applied to stabilization via state feedback, both for the nominal and the uncertain cases.