Mean square robust stability of stochastic switched discrete-time systems with convex polytopic uncertainties

M Rajchakit,G Rajchakit

doi:10.1186/1029-242x-2012-135

Abstract

This article is concerned with mean square robust stability of stochastic switched discrete time-delay systems with convex polytopic uncertainties. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the mean square robust stability for the stochastic switched system with convex polytopic uncertainties is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

Highlights

Since the time delay is frequently viewed as a source of instability and encountered in various engineering systems such as chemical processes, long transmission lines in pneumatic systems, networked control systems, etc., the study of delay systems has received much attention and various topics have been discussed over the past years.A switched system is a hybrid dynamical system consisting of a finite number of subsystems and a logical rule that manages switching between these subsystems
The main approach for stability analysis relies on the use of Lyapunov-Krasovskii functionals and linear matrix inequlity (LMI) approach for constructing a common Lyapunov function [8,9,10]
By using improved Lyapunov-Krasovskii functionals combined with LMIs technique, we propose new criteria for the mean square robust stability of the system

Summary

Introduction

Since the time delay is frequently viewed as a source of instability and encountered in various engineering systems such as chemical processes, long transmission lines in pneumatic systems, networked control systems, etc., the study of delay systems has received much attention and various topics have been discussed over the past years.A switched system is a hybrid dynamical system consisting of a finite number of subsystems and a logical rule that manages switching between these subsystems. The asymptotic stability for switching linear discrete time-delay systems has been studied in [10], but the result was limited to constant delays. This article studies mean square robust stability problem for stochastic switched linear discrete systems with convex polytopic uncertainties with interval time-varying delays.

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Conclusion