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Delay‐dependent stability and H ∞ control of stochastic time‐delay systems with Markovian jumping parameters
Author(s) -
Ma Li,
Da FeiPeng,
Wu Lingyao
Publication year - 2011
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.270
Subject(s) - exponential stability , mathematics , control theory (sociology) , stability (learning theory) , controller (irrigation) , constant (computer programming) , jumping , constraint (computer aided design) , control (management) , computer science , nonlinear system , physics , physiology , geometry , quantum mechanics , artificial intelligence , machine learning , agronomy , biology , programming language
In this paper, the mean‐square exponential stability and H ∞ control problems are investigated for a general class of stochastic time‐delay systems with Markovian jumping parameters. First, a delay‐dependent result in terms of linear matrix inequalities (LMIs) for mean‐square exponential stability and H ∞ performance analysis is presented by constructing a modified Lyapunov‐Krasovskii functional. The decay rate can be chosen in a range to be a finite positive constant without equation constraint. Then, based on the proposed stability result, we derive sufficient condition to solve the H ∞ controller design problem. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society