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In this paper, the problems of finite-time stochastic stability analysis and controller synthesis of uncertain discrete-time Markovian jump linear systems are investigated. The uncertainties considered are that partial elements of the transition probability matrix are not available. By introducing the concept of finite-time stochastic stability for Markovian jump systems, a sufficient condition is proposed to guarantee that the state of the system does not exceed a certain bound in mean square sense during a fixed time interval. It is shown that the system which is not mean square stable may be finite-time stochastically stable and vice versa. For the controller synthesis case, mode-dependent state feedback controller can be developed based on the above stability analysis result. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.