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Delay‐range‐dependent H ∞ control for Markovian jump systems with mode‐dependent time delays
Author(s) -
Wang Guoliang,
Zhang Qingling,
Sreeram Victor
Publication year - 2010
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.247
Subject(s) - control theory (sociology) , exponential stability , lemma (botany) , range (aeronautics) , mathematics , interval (graph theory) , stability (learning theory) , bounded function , mode (computer interface) , control (management) , jump , linear matrix inequality , upper and lower bounds , computer science , nonlinear system , mathematical optimization , mathematical analysis , physics , engineering , combinatorics , quantum mechanics , ecology , poaceae , artificial intelligence , machine learning , biology , aerospace engineering , operating system
This paper considers mean‐square exponential stability and H ∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H ∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society