Global Uniform Asymptotic Stability Criteria for Linear Uncertain Switched Positive Time-Varying Delay Systems with All Unstable Subsystems

Thaned Rojsiraphisal,Piyapong Niamsup,Suriyon Yimnet

doi:10.3390/math8122118

Thaned Rojsiraphisal, Piyapong Niamsup + Show 1 more

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https://doi.org/10.3390/math8122118

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Abstract

In this paper, the problem of robust stability for a class of linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties is investigated. By establishing suitable time-scheduled multiple copositive Lyapunov-Krasovskii functionals (MCLKF) and adopting a mode-dependent dwell time (MDDT) switching strategy, new delay-dependent sufficient conditions guaranteeing global uniform asymptotic stability of the considered systems are formulated. Apart from past studies that studied switched systems with at least one stable subsystem, in the present study, the MDDT switching technique has been applied to ensure robust stability of the considered systems with all unstable subsystems. Compared with the existing results, our results are more general and less conservative than some of the previous studies. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Highlights

Positive systems are systems whose state variables take only non-negative values [1,2,3,4]
In 2019, Feng et al [18] studied the stability and robust stability for linear switched positive systems with all unstable subsystems by utilizing the discretized copositive Lyapunov function and the mode-dependent dwell time (MDDT) switching rule, but the existence of the time-delay was not taken into account
The above discussions motivate us to study the robust stability for a class of continuous-time linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties under the MDDT switching strategy

Summary

Introduction

Positive systems are systems whose state variables take only non-negative values [1,2,3,4]. In 2019, Feng et al [18] studied the stability and robust stability for linear switched positive systems with all unstable subsystems by utilizing the discretized copositive Lyapunov function and the MDDT switching rule, but the existence of the time-delay was not taken into account. The above discussions motivate us to study the robust stability for a class of continuous-time linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties under the MDDT switching strategy. (4) Unlike the existing results in [28,31,36,38,40], the MDDT switching law, which is less conservative and more applicable in practice than the DT switching law, is utilized for the robust stability analysis of the continuous-time linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties in the present study.

Preliminaries

Main Results

Numerical Examples

Conclusions