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IMA Journal of Mathematical Control and Information 2004 21(2):115-141; doi:10.1093/imamci/21.2.115
© 2004 by Institute of Mathematics and its Applications
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LMI approach to robust stability and H{infty} control of uncertain neutral jumping systems

Abdulla Ismail1 and Magdi s. Mahmoud1

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

This paper deals with a general class of uncertain neutral jumping systems with different lengths of distributed state-delays and multiple state-derivative delays. The jumping parameters are treated as a continuous-time, discrete-state Markov process and the uncertainties are parametric and norm-bounded. An LMI-based sufficient condition is provided for the robust stability independent of delay. Then robust stabilization is established using memoryless state feedback and distributed feedback. The results are extended to the nominal neutral jumping and the uncertain retarded systems. Robust H{infty} output feedback control is examined to design observer-based controllers which render the augmented system asymptotically stable independent of delay with a guaranteed performance measure for all admissible uncertainties. All the analytical results throughout the paper are cast into LMI-format. It is shown that the developed results encompass the previously published works as special cases.

Keywords: time-delay systems; linear neutral systems; robust stochastic stability; state-delayed controllers; robust H{infty} control.

Received 6 June 2003.


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