NonfragileH∞Control for Stochastic Systems with Markovian Jumping Parameters and Random Packet Losses

Jing Wang,Ke Zhang

doi:10.1155/2014/934134

Abstract

This paper is concerned with the nonfragileH∞control problem for stochastic systems with Markovian jumping parameters and random packet losses. The communication between the physical plant and controller is assumed to be imperfect, where random packet losses phenomenon occurs in a random way. Such a phenomenon is represented by a stochastic variable satisfying the Bernoulli distribution. The purpose is to design a nonfragile controller such that the resulting closed-loop system is stochastically mean square stable with a guaranteedH∞performance levelγ. By using the Lyapunov function approach, some sufficient conditions for the solvability of the previous problem are proposed in terms of linear matrix inequalities (LMIs), and a corresponding explicit parametrization of the desired controller is given. Finally, an example illustrating the effectiveness of the proposed approach is presented.

Highlights

During the past several decades, stochastic systems have been the main focus of research receiving much attention since realistic models of most engineering systems involve random exogenous disturbances [1, 2]
We will give an LMI approach to solving the nonfragile H∞ control problem formulated in the previous section
We shall introduce the following lemmas, which will be used in the proof of the main results

Summary

Introduction

During the past several decades, stochastic systems have been the main focus of research receiving much attention since realistic models of most engineering systems involve random exogenous disturbances [1, 2]. As a simple yet significant mathematical model, stochastic systems have come to play a key role in many branches of science and engineering [3]. For this reason, many fundamental issues have been extensively addressed for stochastic systems, and fruitful results have been presented in the literature; see, for example, [2, 4, 5] and the references therein. In addition to stochastic systems, there have been great efforts in the research of the modeling of dynamic systems subject to random abrupt changes in their parameters [6,7,8]. Robust stability and stabilization problems were investigated in [18], passivity-based control problem was addressed in [19], optimal control problems were studied in [12, 20,21,22], and the sliding-mode control problem was solved in [23]

Objectives

Results

Conclusion