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Practical stability, controllability and optimal control of stochastic Markovian jump systems with time-delays. (English) Zbl 1153.93535
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:
93E20Optimal stochastic control (systems)
93E12System identification (stochastic systems)
93B05Controllability
60J75Jump processes
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References:
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