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Simultaneous ℋ︁ 2 /ℋ︁ ∞ control of uncertain jump systems with functional time‐delays
Author(s) -
Mahmoud Magdi S.,
Shi Peng,
Boukas El Kebir,
Jain Lakhim
Publication year - 2008
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1221
Subject(s) - control theory (sociology) , mathematics , quadratic equation , upper and lower bounds , norm (philosophy) , controller (irrigation) , jumping , state (computer science) , bounded function , jump , markov process , mathematical optimization , computer science , control (management) , mathematical analysis , algorithm , physiology , physics , quantum mechanics , agronomy , geometry , artificial intelligence , political science , law , biology , statistics
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 ℋ 2 /ℋ ∞ controller which minimizes a quadratic ℋ 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 ℋ 2 /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.