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 and finite-time boundedness of switched linear systems is that each subsystem should be finite-time stable or finite-time bounded. If any one subsystem of switched systems is not finite-time stable or finite-time bounded, the previous results may not be true anymore. In this paper, finite-time stability and finite-time boundedness of switched linear systems with subsystems that are not finite-time stable or finite-time bounded are discussed. Sufficient conditions are given under which switched linear systems with subsystems that are not finite-time stable or finite-time bounded is guaranteed to be still finite-time stable or finite-time bounded. The results also show the effect of the switching signals on finite-time stability and finite-time boundedness of switched linear systems. Moreover, finite-time L₂-gain of switched linear systems with subsystems which are not finite-time bounded is also given to measure its disturbance tolerance capability in the fixed time interval. A numerical example is employed to verify the efficiency of the proposed method.