This article proposes a model predictive control (MPC) design to control a fixed frequency DC-DC power converter in a defined operating domain. The prediction model used for the control synthesis is a piecewise affine approximation (PWA) that covers the whole operating range of the converter. Based on the obtained hybrid model a constrained optimal control problem is formulated and solved. The explicit form of the control law is derived offline as an affine state feedback controller. This explicit controller is stored in a look-up table for implementation. The experimental results show the potential advantages of this control approach in comparison with a static state-feedback or a classic PI controller.