Stability analysis of discrete-time switched linear systems with unstable subsystems

The problem of stability for discrete-time switched linear systems (DSLSs) with unstable subsystems is investigated. Unlike most existing results that require each switching mode of the system to be asymptotically stable, this paper considers the case that each subsystem may be unstable. First, under certain hypotheses, a necessary condition of stability for DSLSs is obtained. Second, using the average dwell time (ADT) strategy, some sufficient conditions of exponential stability for switched linear systems are derived under two assumptions. Finally, two examples are presented to show the effectiveness of the proposed approaches.