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Zbl 1153.93535
Zhao, Ping
Practical stability, controllability and optimal control of stochastic Markovian jump systems with time-delays. (English)
[J] Automatica 44, No. 12, 3120-3125 (2008). ISSN 0005-1098

Summary: The notions of the practical stability in probability and in the $p$th mean, and the practical controllability in probability and in the $p$th mean, are introduced for some stochastic systems with Markovian jump parameters and time-varying delays. Sufficient conditions on such practical properties are obtained by using the comparison principle and the Lyapunov function method. Besides, for a class of stochastic nonlinear systems with Markovian jump parameters and time-varying delays, existence conditions of optimal control are discussed. Particularly, for linear systems, optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters.

MSC 2000:: *93E20 Optimal stochastic control (systems)
93E12 System identification (stochastic systems)
93B05 Controllability
60J75 Jump processes

Keywords: stochastic nonlinear system; Markovian jump parameter; time-delay; practical stability; practical controllability; optimal control

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Zentralblatt MATH Berlin [Germany]