Finite-Time Stability of Switched Linear Time-Delay Systems Based on Time-Dependent Lyapunov Functions

Tiantian Huang,Yuangong Sun

doi:10.1109/access.2020.2977419

Abstract

In this paper, finite-time stability of switched linear time-delay systems has been addressed. By constructing a class of time-dependent common (multiple) Lyapunov functions, new explicit conditions for finite-time stability of the system under arbitrary switching and average dwell-time switching are established respectively. Compared with most of existing results in the literature, our results are easily verifiable by solving several linear matrix inequalities rather than complex matrix Riccati differential equations. The effectiveness of the proposed method is demonstrated by numerical examples.

Highlights

Switched system contains a number of subsystems described by continuous or discrete dynamics, as well as the switching signal regulating the switching between subsystems at each switching time
Since Kamenkov first proposed the concept of finite-time stability, a large number of results have been obtained in the study of FTS of various of systems [4]–[15]
In this paper, finite-time stability of switched linear timedelay systems is studied by constructing a time-dependent

Summary

INTRODUCTION

Switched system contains a number of subsystems described by continuous or discrete dynamics, as well as the switching signal regulating the switching between subsystems at each switching time. Since Kamenkov first proposed the concept of finite-time stability, a large number of results have been obtained in the study of FTS of various of systems [4]–[15]. FTS criteria for a class of switched linear systems were given by constructing a multiple Lyapunov function in [22]. Time-dependent Lyapunov functions may lead to less conservative FTS criteria, they result in unsolvable matrix Riccati differential equations, which is not convenient for the application of the results. We further consider FTS of switched linear systems with time delay by constructing a class of timedependent Lyapunov functions. Sun: FTS of Switched Linear Time-Delay Systems Based on Time-Dependent Lyapunov Functions system under arbitrary switching and average dwell-time switching will be established.

PROBLEM DESCRIPTION AND PRELIMINARIES

NUMERICAL EXAMPLES

CONCLUSION