Finite-time stability of switched nonlinear time-delay systems

This article addresses the problem of finite-time stability (FTS) and finite-time contractive stability (FTCS) for switched nonlinear time-delay systems (SNTDSs). By virtues of the Lyapunov-Razumikhin method, Lyapunov functionals approach, and the comparison principle technique, we obtain some improved Razumikhin-type theorems that verify FTS and FTCS property for SNTDSs. Moreover, our results allow the estimate of the upper bound of the derivatives for Lyapunov functions to be mode dependent functions which can be positive and negative. Meanwhile, the proposed results also improve the related existing results on the same topic by removing some restrictive conditions. Finally, two examples are presented to verify the effectiveness of our methods.