In this paper, the problem of finite-time stochastic stabilization for a class of uncertain Markov jump systems subject to partly known transition probabilities and disturbances is investigated. The constraint on the control input sent to the actuator is also considered. A finite-time stochastic stabilization criterion is given, to ensure that the state trajectory remains in a bounded region of the state space over a fixed time interval in mean square sense. An optimization algorithm is proposed to find the optimal performance and the corresponding feedback controller where the undesirable high-gain phenomenon can be avoided. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.
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