Finite-time stability of switched linear systems with subsystems which are not finite-time stable

Up to now, the potential assumption of most existing results for finite-time stability of switched linear systems is that each subsystem should be finite-time stable. If one subsystem of the switched systems is not finite-time stable, the previous results may fail. In this paper, finite-time stability of switched linear systems with subsystems that are not finite-time stable is discussed. Sufficient conditions are given under which switched linear systems with subsystems that are not finite-time stable are guaranteed to be finite-time stable. The results also show the effect of the switching signals on finite-time stability of switched linear systems. An numerical example is employed to verify the efficiency of the proposed method.