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IMA Journal of Mathematical Control and Information 2003 20(2):179-199; doi:10.1093/imamci/20.2.179
© 2003 by Institute of Mathematics and its Applications
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Output feedback stabilization and disturbance attenuation of time-delay jumping systems

Magdi S. Mahmoud1, Peng Shi2 and Yan Shi3

1 College of Engineering, UAE University, P. O. Pox 17555, Al-Ain, United Arab Emirates 2 Weapons Systems Division, Defense Science and Technology Organisation, PO Box 1500, Edinburgh 5111 SA, Australia 3 Department of Information and Systems Engineering, School of Engineering, Kyushu Tokai University, 9-1-1, Toroku, Kumamoto 862-86852, Japan

The problems of stochastic stabilization and control for a class of linear time-delay systems with Markovian jump parameters via output feedback are investigated. The jumping parameters are modelled as a 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 to be 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{infty}-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. We show that in the case of weak delay-dependency, 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.

Keywords: disturbance attenuation; Markovian jump parameters; output–feedback; stochastic stability; time-delay systems.


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