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IMA Journal of Mathematical Control and Information 2004 21(4):419-431; doi:10.1093/imamci/21.4.419
© 2004 by Institute of Mathematics and its Applications
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State transformation for H{infty} control of uncertain jumping delayed systems

Magdi S. Mahmoud1, Abdulla Ismail1, Peng Shi2,* and Ramesh K. Agarwal3

1 College of Engineering, UAE University, PO Box 17555, Al-Ain, United Arab Emirates, 2 Division of Mathematics and Statistics, School of Technology, University of Glamorgan Pontypridd, Wales, CF37 1DL, UK, 3 Department of Mechanical Engineering, Washington University, Campus Box 1185 St. Louis, MO 63130-4899, USA

A new state transformation exhibiting the delay-dependent behaviour for a class of uncertain delayed systems with Markovian jump parameters is developed to solve the problem of H{infty} control. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state, input and delayed-state matrices. The input and state delays are known. Complete results for instantaneous state feedback control designs are established which guarantee the strong-delay dependent stochastic stability with a prescribed H{infty}-performance. The solutions are provided in terms of a finite set of coupled linear matrix inequalities. A numerical example is given to show the potential of the proposed techniques.

Keywords: time-delay systems; Markovian jump parameters; H{infty} state feedback; stochastic stability; uncertain parameters.

Received 31 July 2003.

* To whom correspondence should be addressed. Email: pshi{at}glam.ac.uk


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