Journal Article

A descriptor approach to simulataneous H<sub>2</sub>/H<sub>∞</sub> control of jumping time‐delay 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 95-114
Published in print June 2004 | ISSN: 0265-0754
Published online June 2004 | e-ISSN: 1471-6887 | DOI: https://dx.doi.org/10.1093/imamci/21.2.95
A descriptor approach to simulataneous H2/H∞ control of jumping time‐delay systems

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In this paper, we develop a descriptor approach to simultaneous H2/H 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‐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∞ control; time‐delay systems; Markovian jump parameters; norm‐bounded uncertainties

Journal Article.  0 words. 

Subjects: Mathematics

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