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

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.