In this paper we investigate the design of controllers, for discrete-time Markovian jump linear systems, that achieve optimal reference tracking in the presence of preview. In particular, given a reference sequence, we obtain the optimal control law for the fully observed case, while the output feedback case is also briefly discussed. We provide the optimal control law for the infinite and finite optimization-horizon cases. The optimal control policy consists of the additive contribution of two terms: a feedforward term and a feedback term which is identical to the standard LQR solution. We provide explicit formulas for computing the feedforward term, while establishing a comparison with the internal model principle
