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Robust finite-time control for a class of extended stochastic switching systems. (English) Zbl 1230.93098
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:
 93E15 Stochastic stability 60J75 Jump processes 93B36 ${H}^{\infty }$-control