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H ∞ control for discrete‐time M arkovian jump systems with partial information on transition probabilities
Author(s) -
Zhang Yan,
He Yong,
Wu Min,
Zhang Jie
Publication year - 2013
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.700
Subject(s) - control theory (sociology) , mathematics , lemma (botany) , weighting , discrete time and continuous time , jump , state (computer science) , stability (learning theory) , mode (computer interface) , control (management) , computer science , algorithm , statistics , physics , ecology , poaceae , quantum mechanics , artificial intelligence , machine learning , biology , operating system , acoustics
This paper focuses on mode‐dependent H ∞ state‐feedback control for a class of discrete‐time M arkovian jump systems ( MJSs ) with partial information on transition probabilities ( TPs ). The augmented free‐connection weighting matrices are introduced by considering the influence of partial information of TPs on discrete‐time MJSs and the disturbance input on the state vector. As a result, the less conservative stability criterion and bounded real lemma ( BRL ) of MJSs with partly unknown TPs are obtained. Then the sufficient conditions for designing the mode‐dependent H ∞ controllers are derived in terms of linear matrix inequalities ( LMIs ). Numerical examples are given to illustrate the effectiveness and the merits of the proposed method.