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STOCHASTIC STABILIZATION AND H ∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS
Author(s) -
Wu Jing,
Chen Tongwen,
Xu Shengyuan
Publication year - 2005
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 - 10.1111/j.1934-6093.2005.tb00232.x
Subject(s) - control theory (sociology) , lemma (botany) , mathematics , discrete time and continuous time , linear matrix inequality , bounded function , state (computer science) , controller (irrigation) , class (philosophy) , jumping , transformation (genetics) , control (management) , mathematical optimization , computer science , algorithm , physiology , ecology , mathematical analysis , statistics , poaceae , artificial intelligence , agronomy , biology , biochemistry , chemistry , gene
In this paper, robust stochastic stabilization and H ∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H ∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.