Dynamics of linear switched systems with disturbances

This paper addresses the dynamics of discrete-time linear switched systems subject to disturbances. The considered systems are with time-varying delays. It is assumed that the nominal systems are exponentially stable and the disturbances satisfy vanishing condition plus one of the following three constraints: Being locally Lipschitz at origin, globally Lipschitz, and differentiable at origin. By “vanishing”, we mean that the disturbance is zero at origin. It is shown that, with these assumptions, the disturbed system is locally exponentially stable if the disturbance is locally Lipschitz at origin or differentiable at origin, is globally stable if the disturbance is globally Lipschitz.