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. K E Y W O R D S finite-time stability, Razumikhin technique, switched nonlinear systems, time-delay systems 1 2906

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Summary This study addresses the uniformly globally asymptotically stability (UGAS) problem of switched nonlinear delay systems (SNDSs) with sampled‐data inputs (SDIs). By using multiple Lyapunov functionals (MLFs) method, mode‐dependent average dwell times, and the total activating time length of MLFs, some stability criteria are explicitly obtained for SNDSs with SDIs. Meanwhile, the UGAS property for SNDSs with some or all unstable modes is investigated. For unstable modes and stable modes, we adopt different switching signals. Besides, we establish some sufficient stability conditions in the form of an upper bound on the sum of dwell times and sampling intervals. Simulation examples are adopted to illustrate and verify the effectiveness of our proposed methods.

This article is concerned with the stability of switched nonlinear time‐delay systems with asynchronous switching. We start by extending the well‐known concept of integral input‐to‐state stability (iISS) to finite‐time integral input‐to‐state stability (FTiISS). It is clear to find that the new concept of FTiISS plays an important role in many branches of engineering and science. Leveraging the Razumikhin‐type theorem along with the average dwell time (ADT) and mode‐dependent ADT methods, sufficient ISS, iISS, finite‐time ISS, and FTiISS criteria for switched nonlinear time‐delay systems under asynchronous switching are presented. Our proposed results improve upon the existing results by removing some restrictive conditions, and subsume some existing ones as special cases. Finally, simulation examples are provided to illustrate the effectiveness and advantages of our results.

This summary addresses the input-to-state stability (ISS) and integral ISS (iISS) problems of impulsive switched nonlinear time-delay systems (ISNTDSs) under two asynchronous switching effects. In our investigated systems, impulsive instants and switching instants do not necessarily coincide with each other. Meanwhile, systems switching signals are not simultaneous with the corresponding controllers switching signals, which will induce instability seriously, and cause many difficulties and challenges. By utilizing methods of Lyapunov-Krasovskii and Lyapunov-Razumikhin, mode-dependent average dwell time approach, and mode-dependent average impulsive interval technique, some stability criteria are presented for ISNTDSs under two asynchronous switching effects. Our proposed results improve the related existing results on the same topic by removing some restrictive conditions and cover some existing results as special cases. Finally, some simulation examples are presented to illustrate the effectiveness and advantages of our results. K E Y W O R D S impulsive switched systems, input-to-state stability, nonlinear time-delay systems, two asynchronous switching phenomena.