In this report, we present a Model Predictive Controller (MPC) based on Linear Matrix Inequalities (LMI’s). As in the standard MPC algorithms, at each (sampling) time, a convex optimization problem is solved to compute the control law. The optimization involves constraints written as LMI’s, including those normally associated to MPC problems, such as input and output limits. Even though a state space representation is used, only the measurable output and some statistic properties of the non measurable states are used to determine the controller, hence it is an output feedback control design method. Stability of the closed loop system is demonstrated. The design technic is illustrated with a numerical example.