Stability analysis of switched nonlinear delay systems with sampled‐data inputs

Abstract

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.

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

“…1 In recent years, there has been a rich body of research results reported in the existing works about switched systems due to their widespread and successful applications in many branches of engineering and science practical systems, such as multi-agent systems, 2 robotic systems, 3 and networked control systems. 4 But, those results all have a common assumption that the states of those subsystems do not jump at the switching moments. Meanwhile, the motivation for investigating switched systems is also for that many industrial practical systems can not be represented as signal mode systems and utilize the switching strategy to improve their performance.…”

Finite‐time stability of switched nonlinear time‐delay systems

“…8 Based on the ADT approach, the stability for slow switching systems was investigated in the work of Niu et al 9 Moreover, the mode-dependent ADT (MDADT) method was proposed by Zhao et al 10 to address the stability for SNSs with unstable subsystems. 11,12 By the MDADT method, some sufficient conditions of the stability were obtained for switched nonlinear time-delay systems (SNTDSs) with sampled-data controllers in the work of Wang et al 13 In addition, Wang et al 14 utilized the sampled integral stabilization technique to address the stabilization problem for SNSs. Furthermore, based on a new mode-dependent intermediate variable, the fault estimation problem for nonlinear semi-Markovian jump systems was investigated in the work of Liang et al 15 By utilizing a new time-scheduled Lyapunov functional, Chen et al 16 obtained mean square exponential stability criteria and the sampled-data controller for sampled-data Markovian jump systems.…”

Sampled‐data exponential stabilization of switched nonlinear delayed systems with asynchronous switching

“…14 Consequently, many valuable results were obtained with the assistance of ADT method. [15][16][17][18][19][20][21][22][23][24] For instance, based on the mode-dependent ADT method and the Lyapunov functional method, Reference 21 derived the exponential synchronization criteria for delayed switched neural networks. With the aid of multiple LKFs and ADT approach, Reference 22 investigated the absolute exponential stability of switched nonlinear delayed systems (SNDSs).…”