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. [ABSTRACT FROM AUTHOR]