Finite-time stability analysis of switched nonlinear systems with finite-time unstable subsystems

Up to now, the precondition that each subsystem should be finite-time stable is potentially guaranteed in most existing results for the finite-time stability research of switched systems. If one subsystem of the switched systems is not finite-time stable, the previous results may not work. In this paper, based on Lyapunov-like functions, the finite-time stability problem of switched nonlinear systems with subsystems that are not finite-time stable is discussed. Sufficient conditions are given under which switched nonlinear systems with subsystems that are finite-time unstable are guaranteed to be still finite-time stable by virtue of common Lyapunov-like function and multiple Lyapunov-like functions respectively. The results also show the effect of switching signals and the total dwell time of finite-time unstable subsystems on finite-time stability of switched nonlinear systems. A numerical example is employed to verify the efficiency of the proposed method.