This article proposes a controller using Fuzzy Model Predictive Control (FMPC) and a fuzzy state observer applied to a three states switching cell (3SSC) boost converter. The proposed approach is an observer-based output feedback fuzzy MPC, which combines a state feedback FMPC controller with a fuzzy state observer. Moreover, a stability criterion is developed for the controller-observer procedure, considering a Takagi-Sugeno (T-S) fuzzy model, a PDC fuzzy control law, a fuzzy state observer and a state feedback FMPC, through the Linear Matrix Inequalities (LMI) optimization procedure. Furthermore, an Anti-Windup (AW) procedure is added to the control scheme. The proposed procedure is implemented for a boost converter through computer simulation, and the obtained results are compared with two MPC controllers. The analysis is done considering the time response and some performance indexes, moreover, the robust stability for the studied controller is explicit using stability ellipsoids.