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SLQC for discrete-time Markovian jump stochastic linear systems

In this paper, the problem of the optimization of a quadratic cost functional along the trajectories of a discrete-time stochastic linear systems with Markovian jump is investigated. The case of finite time horizon is considered. A suitable solution for a system of discrete-time Riccati type equations is used to construct the optimal control. After some useful auxiliary results given in this paper, the problem of the optimization of a discrete-time stochastic linear systems with Markovian jump in the finite time horizon case is solved.