Finite‐time stability of switched nonlinear time‐delay systems

Abstract

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

Finite‐time integral input‐to‐state stability for switched nonlinear time‐delay systems with asynchronous switching

“…Switched time‐delay systems are natural generalizations of switched systems and have strong engineering background. Recently, switched systems with time delays have attracted considerable attention, and some efforts have been made to extend the stability results for switched systems to switched time‐delay systems 2,12,13 . As is well known, there are mainly two approaches in dealing with time‐delay systems, namely, the Lyapunov–Razumikhin method and the Lyapunov–Krasovskii method 9,14 .…”

Finite‐time energy‐to‐peak quantized filtering for Markov jump networked systems under weighted try‐once‐discard protocol

“…Through employing Schur complement to (27), it is clearly found that Ψ m <0. In addition, condition (27) implies that…”

Input‐to‐state stability of impulsive switched nonlinear time‐delay systems with two asynchronous switching phenomena

“…Moreover, time delays are also generally recognized as a source of performance debasement and instability of dynamic systems. [7][8][9][10] For example, Chen et al 9 investigated the influence of time delays on the robust sampled-data control for Itô stochastic Markovian jump systems with state delay. In fact, impulsive switched nonlinear time-delay systems (ISNTDSs) are ubiquitous in many branches of engineering and science such as power electronic systems, economic models, epidemic models, and mechanical rotational cutting process.…”

“…Meanwhile, time delays are inevitable in models describing engineering processes because of a variety of reasons such as the finite speed of information processing, vast amounts of data, and inherent phenomena. Moreover, time delays are also generally recognized as a source of performance debasement and instability of dynamic systems 7-10 . For example, Chen et al 9 investigated the influence of time delays on the robust sampled‐data control for Itô stochastic Markovian jump systems with state delay.…”