Finite-Time Stability and Stabilization of Switched Linear Time-Varying Systems with Time-Varying Delay

Lulu Feng,Ping Zhao,Delfim Soares Jr

doi:10.1155/2021/8880744

Lulu Feng, Ping Zhao + Show 1 more

Open Access

https://doi.org/10.1155/2021/8880744

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Abstract

This paper deals with the finite-time stability (FTS) of switched linear time-varying (SLTV) systems with time-varying delay. Firstly, based on Lyapunov–Krasovskii functional technique and average dwell time (ADT) approach, a sufficient criterion on FTS for SLTV systems with time-varying delay is obtained. For the SLTV system with delay and control input, based on the criterion, a state feedback controller is designed such that the closed-loop system is finite-time stable (FTS). Finally, an example is employed to illustrate the validity of our results.

Highlights

Switched systems are a special kind of hybrid dynamical systems, which consist of several subsystems and a switching law that orchestrates the switching between the subsystems [1]
Due to large state amplitude in the transient process, some asymptotic stable systems may be useless. us, it is more meaningful to study the stability in a fixed time interval. e concept of finite-time stability (FTS) was first introduced in 1960s [8, 9]
The main contributions of this paper can be summarized as follows: (1) sufficient conditions on FTS of the switched system will be given under the case of linear time-varying (LTV) systems; (2) a state feedback controller will be designed for the switched linear time-varying (SLTV) system with time-varying delays

Summary

Introduction

Switched systems are a special kind of hybrid dynamical systems, which consist of several subsystems and a switching law that orchestrates the switching between the subsystems [1]. A system is said to be finitetime stable (FTS) if its state does not exceed a certain bound during a specified time interval for a given bound on the initial condition For such stability, there are many practical applications such as networked control systems [10] and network congestion control [11]. Erefore, in this paper, we analyze FTS of SLTV systems with time-varying delays using the Lyapunov–Krasovskii functional method. The main contributions of this paper can be summarized as follows: (1) sufficient conditions on FTS of the switched system will be given under the case of LTV systems; (2) a state feedback controller will be designed for the SLTV system with time-varying delays.

Preliminaries

Finite-Time Stability Analysis

Finite-Time Stability via State Feedback

Numerical Example