Stability and Controller Synthesis of Discrete Linear-Switched Systems

Abstract

Sufficient conditions are presented for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic-type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterward. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case, where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l2 -gain analysis where a bounded real lemma is derived, and to H∞ control and estimation, both for the nominal and the uncertain cases.