Robust Stability Analysis for Uncertain Switched Discrete-Time Systems

Yali Dong

doi:10.1155/2011/523020

Abstract

This paper is concerned with the robust stability for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Highlights

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
Switched systems have drawn a great deal of attention in recent years, see 1–24 and references therein
Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function

Summary

Introduction

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 problem of stability analysis and control synthesis of switched systems in the discrete-time domain was addressed in 11. Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function. These two conditions have been proved to be equivalent for stability analysis. The objective of this paper is to present novel approaches for the asymptotical stability of switched discrete-time system with parametric uncertainties. A new sufficient condition for robust stability of a class of uncertain switched discrete-time systems is proposed. Using the block matrix method, inequality technology, and the Lyapunov stability theorem, some sufficient conditions for robust stability have been presented for the uncertain switched discrete-time systems, and the switched law design has been performed.

Systems Description and Problem Statement

We have βi

Stability Analysis of Uncertain Switched Discrete-Time System

Numerical Examples

Conclusion