Output Feedback Stabilization and Disturbance Attenuation of Time-Delay Systems with Markovian Jump Parameters

A. Ismail, M.S. Mahmoud, and P. Shi

Keywords

Disturbance attenuation, Markovian jump parameters, outputfeedback, stochastic stability, timedelay systems

Abstract

This article investigates the problems of stochastic stabilization and control for a class of linear time-delay systems with Markovian jump parameters via output feedback. The jumping parameters are modelled as continuous-time, discrete-state Markov process. The delay factor is unknown and time-varying with a known bound. Concepts of weak and strong delay-dependent stochastic stability are introduced, and appropriate criteria applied to the jumping systems are developed. The control objective is to design an output-feedback controller such that stochastic stability and a prescribed H∞-like performance for a closed-loop system are guaranteed. We establish that the stability and stabilization problems for the time-delay Markovian jump systems can be essentially solved in terms of the solutions of a finite set of coupled linear matrix inequalities (LMIs). We show that in the case of weak delay-dependence, the controller is of arbitrary order and the associated gain matrices are computed implicitly. In the case of strong–weak coupling the controller is of full-order and explicit expressions are given for the associated gain matrices.

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