New Results on Finite-Time Stability and Stabilization of Switched Positive Linear Time-Delay Systems

Xudong Zhao,Ning Xu,Guangdeng Zong,Li-Juan Liu

doi:10.1109/access.2019.2961683

Abstract

In this paper, the problems of finite-time stability and stabilization for switched positive linear time-delay systems under mode-dependent average dwell time (MDADT) are investigated. By proposing a novel multiple piecewise copositive Lyapunov-Krasovskii functional, new results on the sufficient conditions of finite-time stability are obtained. In order to solve the limitation of the multiple piecewise copositive Lyapunov-Krasovskii functional on designing controllers, a novel linear combinatorial copositive Lyapunov-Krasovskii functional is constructed, this provides a possibility for the numerical construction of the controller. Then by using state feedback controller, the finite-time stabilization is achieved. Finally, some simulation results are given to show the advantages of our methods.

Highlights

Switched systems consist of several subsystems described by differential or difference equations and a switching signal orchestrating the switching among these subsystems
The construction idea of this linear combinatorial copositive Lyapunov-Krasovskii functional method can be extended to the construction of linear combinatorial copositive Lyapunov function, so as to solve the problems such as the numerical construction forms of controllers or observers
In order to solve the limitation that multiple piecewise copositive Lyapunov function method cannot be used to design controller, the construction idea of this linear combinatorial copositive Lyapunov-Krasovskii functional method can be extended to the construction of linear combinatorial copositive Lyapunov function, so as to solve the problems such as the numerical construction forms of controllers or observers

Summary

Introduction

Switched systems consist of several subsystems described by differential or difference equations and a switching signal orchestrating the switching among these subsystems. Due to the importance of switched systems in theoretical development and practical application, switched systems have attracted much attention from scholars [1]–[6], [7]. When the initial condition is non-negative, the state is always limited to non-negative. Such system is called a positive system. In recent decades, switched positive systems have attracted the wide interest of scholars because switching signals determine the switching rules among multiple positive subsystems. The study of such systems does meet the practical needs of different fields, such as ecology, industrial engineering, communications and so on [8]–[10]. The study of such systems does meet the practical needs of different fields, such as ecology, industrial engineering, communications and so on [8]–[10]. [11] and [12] have studied the stability problem for continuous-time switched

Objectives

Results

Conclusion