RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

Shengchun Yu,Guici Chen,Yi Shen

doi:10.1155/2013/163769

Abstract

The robustH∞control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robustH∞controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robustH∞controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robustH∞controller.

Highlights

In the past few years, much research effort has paid to the robust control problems for stochastic systems which have come to play an important role in many fields including communication network, image processes, and mobile robot localization
Xu et al [13] investigate the problems of robust stochastic stabilization and robust H∞ control for uncertain neutral stochastic timedelay systems
Inspired by the above discussions, in this paper we study the robust H∞ control problem for discrete-time stochastic interval system (DTSIS) with time delay

Summary

Introduction

In the past few years, much research effort has paid to the robust control problems for stochastic systems which have come to play an important role in many fields including communication network, image processes, and mobile robot localization. The stability analysis and robust control for dynamic time-delay systems have attracted a number of researchers; see, for example, [4– 8] and the references therein. In the view of dissipation, Berman develops a H∞-type theory for a large class of time-continuous stochastic nonlinear systems. It introduces the notion of stochastic dissipative systems by analogy with the familiar notion of dissipation associated with the deterministic systems. The problem of H∞ output feedback control for uncertain stochastic systems with time-varying delay is discussed in [12], and the parameter uncertainties are assumed to be time-varying norm-bounded. Xu et al [13] investigate the problems of robust stochastic stabilization and robust H∞ control for uncertain neutral stochastic timedelay systems

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Conclusion