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Zbl 1230.93098
Luan, Xiaoli; Liu, Fei; Shi, Peng
Robust finite-time control for a class of extended stochastic switching systems. (English)
[J] Int. J. Syst. Sci. 42, No. 7, 1197-1205 (2011). ISSN 0020-7721; ISSN 1464-5319/e

Summary: This article proposes a new design approach for robust finite-time $H _{\infty }$ control of a class of Markov jump systems with partially known information on the transition jump rates. The system under consideration involves norm-bounded parameter uncertainties and external disturbance. The problems of robust finite-time boundedness and finite-time stabilisation of the underlying systems are considered. Then, a $H _{\infty }$ state feedback controller is designed. Sufficient conditions that consider only the known bounds on the transition jump rates are developed in the form of linear matrix inequalities. A numerical example is included to show the usefulness of the theoretic results obtained.

MSC 2000:: *93E15 Stochastic stability
60J75 Jump processes
93B36 $H^\infty$-control

Keywords: Markov jump systems; unknown jump rates; finite-time boundedness; finite-time stabilisation; $H _\infty $ control

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Zentralblatt MATH Berlin [Germany]