Robust Exponential Stability for Uncertain Discrete-Time Switched Systems with Interval Time-Varying Delay through a Switching Signal

Abstract

This paper deals with the switching signal design to robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay. The lower and upper bounds of the time-varying delay are assumed to be known. By construction of a new Lyapunov-Krasovskii functional and employing linear matrix inequality, some novel sufficient conditions are proposed to guarantee the global exponential stability for such system with parametric perturbations by using a switching signal. In addition, some nonnegative inequalities are used to provide additional degrees of freedom and reduce the conservativeness of systems. Finally, some numerical examples are given to illustrate performance of the proposed design methods.

H∞ filtering of discrete‐time switched singular systems with time‐varying delays

“…[9][10][11] As far as we know, switched systems belong to a hybrid dynamical system, which consist of a finite number of continuous or discrete-time subsystems and a logical rule that supervises the switching between these subsystems at each instant of time. 12 However, many practical processes can be modeled as switched systems, such as control of mechanical systems, power systems, chemical processes, network control systems, embedded systems, power electronics, automate highway systems, constrained robotics, robot manufacture, and various other fields [12][13][14][15][16][17][18] and the references therein. Over the past few decades, many advanced approaches have been proposed to study the problems of stability and stabilization of switched linear systems with or without time-delay; see, e.g.…”

Robust stability and H∞ control for nonlinear discrete‐time switched systems with interval time‐varying delay

“…However, as time goes by, discrete‐time switched systems have gained more importance among researchers focusing on switched systems. During the last decade, there have been many studies on stability analysis and H ∞ controller synthesis for discrete‐time switched systems . In the study of Rajchakit et al, the sufficient conditions for robust stability and stabilization of a class of uncertain switched discrete‐time systems were presented.…”

“…During the last decade, there have been many studies on stability analysis and H ∞ controller synthesis for discrete-time switched systems. [16][17][18][19][20][21] In the study of Rajchakit et al, 16 the sufficient conditions for robust stability and stabilization of a class of uncertain switched discrete-time systems were presented. In the study of Arunkumar et al, 17 stability of switched nonlinear systems with delay and disturbance was investigated.…”

“…In the study of Arunkumar et al, stability of switched nonlinear systems with delay and disturbance was investigated. In the study of Chen et al, robust exponential stability for uncertain discrete‐time switched systems with interval time‐varying delay was addressed. In the study of Rajchakit M and Rajchakit G, mean square robust stability of stochastic switched discrete‐time systems with convex polytopic uncertainties was considered.…”

Finite-time H ∞ state estimation for switched neural networks with time-varying delays

“…It was well known that the ADT scheme characterizes a large class of stable switching signals than dwell time scheme, and its extreme case is the arbitrary switching. Thus, the ADT method is very important not only in theory, but also in practice, and considerable attention has been paid, and a lot of efforts have been done to take advantage of the ADT method to investigate the stability and stabilization problems both in linear and nonlinear systems (see [28]- [32]). The concept of "dwell time" is extended to the concept of "average dwell time".…”