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Finite-time stability of switched systems

The finite-time stability of switched linear systems which contain both Hurwitz stable subsystems and unstable subsystems is researched in this paper. Firstly, the definition of finite-time stability is introduced. Then, based on the average dwell-time concept and by using the idea of specifying the total activation time period ration between the Hurwitz stable subsystems and unstable subsystems, some sufficient conditions for the finite-time stability are gotten. The problem of switched nonlinear systems through designing state feedback controllers is also studied. The sufficient conditions for finite-time stability of switched nonlinear systems are expressed through the forms of polynomial matrix inequalities which can be solved by means of SOSTOOLS. Finally, two examples are presented to show the validity of the results.