H∞Control for Stochastic Systems with Markovian Switching and Time-Varying Delay via Sliding Mode Design

Lijun Gao,Yuqiang Wu

doi:10.1155/2013/898172

Abstract

This paper addresses the problem ofH∞control for a class of uncertain stochastic systems with Markovian switching and time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties and an unknown nonlinear function in the state. An integral sliding surface corresponding to every mode is first constructed, and the given sliding mode controller concerning the transition rates of modes can deal with the effect of Markovian switching. The synthesized sliding mode control law ensures the reachability of the sliding surface for corresponding subsystems and the global stochastic stability of the sliding mode dynamics. A simulation example is presented to illustrate the proposed method.

Highlights

Many practical dynamics, for example, manufacturing systems, chemical process systems, computer controlled systems and communication systems, solar receiver control, and power systems, experience abrupt random changes in their structure
This paper addresses the problem of H∞ control for a class of uncertain stochastic systems with Markovian switching and timevarying delays
This section constructs an SMC law u(t) for system (5)–(7) such that the resultant closed-loop system is stochastically stable despite uncertainties, exogenous disturbance, time delay, and Markovian switching

Summary

Introduction

For example, manufacturing systems, chemical process systems, computer controlled systems and communication systems, solar receiver control, and power systems, experience abrupt random changes in their structure These changes are usually caused by random failure or repairs of the components, changing in subsystems interconnections, sudden environmental changes, and so forth. Chang [15] developd an SMC method to guarantee the robust state covariance assignment for perturbed stochastic multivariable systems via variable structure control. Niu et al [17] paid some efforts to coping with the connection among the designed sliding surface corresponding to every mode for MJSs. there are little results reported on the SMC of stochastic systems with Markovian switching. This paper studies the robust H∞ control problem for uncertain stochastic systems with time-varying delays and Markovian switching. SMC law is synthesized to guarantee that the trajectories can be driven onto the specified sliding surfaces for each mode in finite time and the dynamics along the sliding surface for each mode is stochastically stable

Preliminaries

Main Results

Stochastic Stability of Sliding Surface

Simulation Example

Conclusions