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

Authors: Chafea Haddad; Saïd Djennoune; Maamar Bettayeb

Addresses: Laboratoire de Conception et Conduite des Systèmes de Production, University Mouloud Mammeri of Tizi-Ouzou, Algeria ' Laboratoire de Conception et Conduite des Systèmes de Production, University Mouloud Mammeri of Tizi-Ouzou, Algeria ' Department of Electrical and Computer Engineering, University of Sharjah, United Arab Emirates; Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, Saudi Arabia

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.

Keywords: Markov jump systems; robust cotrol; decentralised control; H-infinity control; state feedback; discrete time systems; random abrupt changes; bounded transition probabilities; linear matrix inequalities; LMIs; uncertainty; controller design; numerical simulation.

DOI: 10.1504/IJMIC.2015.072988

International Journal of Modelling, Identification and Control, 2015 Vol.24 No.4, pp.267 - 280

Accepted: 20 Apr 2015
Published online: 11 Nov 2015 *

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