The goal of this talk is to consider the control of discrete-time Markov Jump Linear Systems (MJLS) assuming partial information on the state variable and\or the Markov jump parameter. It is assumed that there is a detector that emits signals which provides information on the Markov parameter, covering the extreme cases of perfect information and no information at all on the Markov parameter. The idea is to use the information provided by this detector in order to design a controller that stochastically stabilizes the closed loop MJLS with a guaranteed upper bound cost. A Linear Matrix Inequalities formulation is provided in order to achieve this goal.