H∞ control for sampled-data linear systems with two Markov processes

Abstract

This paper is concerned with the design problem of H∞ digital switching control for linear continuous systems with Markovian jumping parameters. The controller is digital and monitored by the jumping parameters of the plant. The closed-loop system is a hybrid one defined on a hybrid time space (composed of a continuous-time and a discrete-time) and a sample space. The sample space is specified by two separable continuous-time discrete-state Markov processes, one appearing in the open-loop system, and the other appearing in control action, which is different with the traditional Markovian jumping process. Our attention is focused on designing digital output feedback controllers for the system with two Markovian jumping processes such that both stochastic stability and a prescribed H∞ performance are achieved. The problem of robust H∞ control for systems with parameters uncertainties is also studied. It is shown that the sampled-data control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled matrix inequalities. Two numerical examples are given to show the design procedures. Copyright © 2005 John Wiley & Sons, Ltd.