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Type: Journal article
Title: Simultaneous H₂/H∞ control of uncertain jump systems with functional time-delays
Other Titles: Simultaneous H(2)/H infinity control of uncertain jump systems with functional time-delays
Author: Mahmoud, M.
Shi, P.
Boukas, E.
Jain, L.
Citation: International Journal of Robust and Nonlinear Control, 2008; 18(3):296-318
Publisher: John Wiley & Sons Ltd
Issue Date: 2008
ISSN: 1049-8923
Statement of
Magdi S. Mahmoud, Peng Shi, El Kebir Boukas and Lakhim Jain
Abstract: This paper presents new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state in which the time-delays are mode dependent. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the uncertainties are norm-bounded. We construct an appropriate Lyapunov-Krasovskii functional and design a simultaneous ℋ2/ℋ∞ controller which minimizes a quadratic ∞2 performance measure while satisfying a prescribed ℋ∞-norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the simultaneous ℋ2/ℋ∞ controller and the associated performance upper bound are cast in the form of linear matrix inequalities. Simulation results are provided and extension to the case where the jumping rates are subject to uncertainties is presented. Copyright © 2007 John Wiley & Sons, Ltd.
Keywords: state-delay systems
Markovian jump parameters
simultaneous H2/Hinfinity control
stochastic stability
norm-bounded uncertainties
Rights: Copyright © 2007 John Wiley & Sons, Ltd.
DOI: 10.1002/rnc.1221
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Electrical and Electronic Engineering publications

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