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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 pth mean, and the practical controllability in probability and in the pth 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.
93E20Optimal stochastic control (systems)
93E12System identification (stochastic systems)
60J75Jump processes