Observer-Based Finite-TimeH∞Control of Singular Markovian Jump Systems

Yingqi Zhang,Wei Cheng,Xiulan Guo,Xiaowu Mu

doi:10.1155/2012/205727

Abstract

This paper addresses the problem of finite-timeH∞control via observer-based state feedback for a family of singular Markovian jump systems (SMJSs) with time-varying norm-bounded disturbance. Firstly, the concepts of singular stochastic finite-time boundedness and singular stochastic finite-timeH∞stabilization via observer-based state feedback are given. Then an observer-based state feedback controller is designed to ensure singular stochastic finite-timeH∞stabilization via observer-based state feedback of the resulting closed-loop error dynamic SMJS. Sufficient criteria are presented for the solvability of the problem, which can be reduced to a feasibility problem involving linear matrix inequalities with a fixed parameter. As an auxiliary result, we also discuss the problem of finite-time stabilization via observer-based state feedback of a class of SMJSs and give sufficient conditions of singular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs. Finally, illustrative examples are given to demonstrate the validity of the proposed techniques.

Highlights

There exist many concerned problems which described that system state does not exceed some bound during some time interval, for instance, large values of the state are not acceptable in the presence of saturations 1–3
We investigate the problem of observer-based finitetime stabilization via state feedback of a class of SMJSs and give sufficient conditions of singular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs
This paper investigates the problem of finite-time H∞ control via observer-based state feedback for a family of SMJSs with time-varying norm-bounded disturbance

Summary

Introduction

There exist many concerned problems which described that system state does not exceed some bound during some time interval, for instance, large values of the state are not acceptable in the presence of saturations 1–3. To date, the problems of observer-based finite-time stabilization of singular stochastic systems have not been investigated. We consider the problem of finite-time H∞ control via observer-based state feedback of singular Markovian jump systems SMJSs with time-varying normbounded disturbance. The main contribution of the paper is to design an observer-based state feedback controller which ensures singular stochastic finitetime H∞ stabilization via observer-based state feedback of the resulting closed-loop error dynamic SMJS. We investigate the problem of observer-based finitetime stabilization via state feedback of a class of SMJSs and give sufficient conditions of singular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs. The rest of this paper is organized as follows. Notations sup and inf denote the supremum and infimum, respectively Matrices, if their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations

Problem Formulation

Main Results

Numerical Examples

Conclusions