Exponential stability of discrete-time systems with slowly time-varying delays. (November 2022)

• Record Type: Journal Article
• Authors: Chen, Da; Liu, Xingwen; Shi, Kaibo; Shao, Shiquan; Wang, Huazhang
• Is Part Of: Nonlinear analysis. Volume 46(2022)
• Publication Date: 2022-11
• Subjects: Discrete-time systems -- Exponential stability -- Switching transformation approach -- Switched homogeneous polynomial Lyapunov function -- Slowly time-varying delays; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2022.101246
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.