Journal Article

LMI approach to robust stability and H<sub>∞</sub> control of uncertain neutral jumping systems

Abdulla Ismail and Magdi s. Mahmoud

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 2, pages 115-141
Published in print June 2004 | ISSN: 0265-0754
Published online June 2004 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/21.2.115
LMI approach to robust stability and H∞ control of uncertain neutral jumping systems

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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 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∞ control

Journal Article.  0 words. 

Subjects: Mathematics

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