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IMA Journal of Mathematical Control and Information 2004 21(2):95-114; doi:10.1093/imamci/21.2.95
© 2004 by Institute of Mathematics and its Applications
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A descriptor approach to simulataneous H2/H{infty} control of jumping time-delay systems

Abdulla Ismail1 and Magdi S. Mahmoud1

1 College of Engineering, UAE University, PO Box 17555, Al-Ain, United Arab Emirates

In this paper, we develop a descriptor approach to simultaneous H2/H{infty} control design for a class of uncertain time-delay systems with Markovian jump parameters. The rationale behind this approach is to exhibit the delay-dependence dynamics in the design procedure. In the system under consideration, the delay factor is constant, the jumping parameters are modelled as a continuous-time, discrete-state Markov process and the uncertainties are assumed to be real, time-varying and norm-bounded. A state-feedback control is derived for both the nominal and uncertain systems such that the H2-performance measure is minimized while guaranteeing a prescribed H{infty}-norm bound on the controlled system. All the developed results are cast in the format of linear matrix inequalities (LMIs) and numerical examples are presented.

Keywords: simultaneous H2/H{infty} control; time-delay systems; Markovian jump parameters; norm-bounded uncertainties.

Received 9 June 2003.


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