Robust H<inf>∞</inf> control of discrete-time Markov jump uncertain systems with bounded transition probabilities

Abstract

In this paper, the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem is investigated for a class of discrete-time Markov jump uncertain systems subject to unknown transition probabilities. Previous results assume that the transition probabilities are completely known. Here, the more general situation where only upper and lower bounds of theses transition probalities are known. Robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller is constructed that guarantee stochastic stabilization of the closed-loop uncertain system under the bounded transition probabilities for all admissible uncertainties. The solution of this control problem is obtained following the Linear Matrix Inequalities (LMI) technique. A numerical simulation example is given to illustrate the main results developed in this paper.