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Sliding mode H ∞ control of time‐varying delay Markov jump with quantized output
Author(s) -
Zhang Hainan,
Shen Mouquan
Publication year - 2018
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.2475
Subject(s) - control theory (sociology) , reachability , sliding mode control , observer (physics) , controller (irrigation) , nonlinear system , state observer , mathematics , upper and lower bounds , computer science , control (management) , algorithm , mathematical analysis , physics , quantum mechanics , artificial intelligence , agronomy , biology
Summary This paper investigates the quantized sliding mode control of Markov jump systems with time‐varying delay. A dynamical adjustment law is explored to quantize the system output. By constructing an observer‐based integral sliding surface, a sliding mode controller is designed to take over the dynamical motion of state estimation and ensure the reachability of sliding surface. A new scaling manner is developed to build the bound between the system output and quantized error. With the help of separation strategies for controller synthesis and general transition probabilities and a lower bound theorem for nonlinear integral terms, a new synthesis method to ensure the required stability and meet the required H ∞ performance is proposed in the form of linear matrix inequalities. The validity of the proposed control method is illustrated by a numerical example.