Robust decentralised H∞ control of discrete-time Markov jump interconnected systems with bounded transition probabilities

Abstract

This paper deals with the problem of robust H∞ control via decentralised state feedback for a class of uncertain interconnected discrete-time Markov jump systems subject to unknown transition probabilities. The uncertainties are assumed to satisfy the global Lipschitz conditions, and the random parameter is a Markov process. A sufficient condition is developed to design controllers via local system states and local operation modes that guarantee stochastic stabilisation of the closed-loop decentralised uncertain system under the bounded transition probabilities for all admissible uncertainties. The solution of this control problem is obtained following the linear matrix inequalities (LMIs) technique. A numerical simulation example is given to illustrate the main results developed in this paper.