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New results on H ∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information
Author(s) -
Wei Yanling,
Qiu Jianbin,
Karimi Hamid Reza,
Wang Mao
Publication year - 2013
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.2093
Subject(s) - control theory (sociology) , linearization , output feedback , jump , constant (computer programming) , computer science , discrete time and continuous time , controller (irrigation) , interconnection , mathematics , nonlinear system , control (management) , computer network , statistics , artificial intelligence , agronomy , biology , programming language , physics , quantum mechanics
SUMMARY This paper investigates the problem of delay‐dependentH ∞dynamic output feedback control for a class of discrete‐time Markovian jump linear systems (MJLSs). The systems under consideration are subject to time‐varying delay and defective mode information. The defective transition probabilities comprise of three types: exactly known, uncertain, and unknown. By employing a two‐term approximation for the time‐varying delay, the original MJLSs can be equivalently converted into a feedback interconnection form, which contains a forward subsystem with constant time‐delays and a feedback one with norm‐bounded uncertainties. Then, based on the scaled small‐gain theorem, the problem is therefore recast as anH ∞control problem in the face of uncertainties via an input–output framework. It is shown that the explicit expressions of the desired controller gains can be characterized in terms of strict linear matrix inequalities via some linearization techniques. Simulation studies are performed to illustrate the effectiveness and less conservatism of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.