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In this paper, we propose a novel approach to the modeling and controller design of the synchronous step-down dc-dc converter. We introduce a hybrid converter model that is valid for the whole operating regime and captures the different modes of operation. Based on this model, we formulate and solve a constrained optimal control problem. This allows a systematic controller design that achieves the regulation of the output voltage to its reference despite input voltage and output load variations while satisfying the constraints on the duty cycle and the inductor current. The resulting state-feedback control law is of piecewise affine form, which can be easily stored and implemented in a lookup table. A Kalman filter is added to account for unmeasured load variations and to achieve zero steady-state output voltage error. Experimental results demonstrate the potential advantages of the proposed control methodology.