Abstract
In this paper we consider the stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a necessary and sufficient condition under which the problem is well-posed and a state feedback solution can be derived from a set of coupled generalized Riccati difference equations interconnected with a set of coupled linear recursive equations.
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