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H ∞ control for discrete‐time Markovian jump linear systems with partially uncertain transition probabilities
Author(s) -
Sun HuiJie,
Zhang Ying,
Wu AiGuo
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2644
Subject(s) - control theory (sociology) , mathematics , markov process , jump , controller (irrigation) , stability (learning theory) , state (computer science) , work (physics) , discrete time and continuous time , full state feedback , control (management) , computer science , engineering , physics , algorithm , mechanical engineering , statistics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
Summary This work is concerned with the H ∞ state‐feedback control for the discrete‐time Markovian jump systems with incomplete knowledge of transition probabilities. A less conservative criterion is proposed via linear matrix inequalities (LMIs) such that the considered systems are stochastically stable and have a prescribed H ∞ disturbance attention level. Furthermore, based on the obtained results, a state‐feedback controller is presented via LMIs to guarantee the stochastic stability of the resulted closed‐loop system with a prescribed H ∞ performance level γ . The number of the LMIs to be solved in the developed methods is much less than that in many existing methods. A numerical example and a practical example are provided to verify the effectiveness of the presented methods.