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DC-DC converters pose challenging hybrid control problems, since the semiconductor switches induce different modes of operation and several constraints (on the duty cycle and the inductor current) are present. In this paper, we propose a novel approach to the modeling and controller design problem for fixed-frequency DC-DC converters, using a synchronous step-down DC-DC converter as an illustrative example. We introduce a hybrid converter model that is valid for the whole operating regime. Based on this model, we formulate and solve a constrained optimal control problem. To make the scheme implementable, we derive offline the explicit state-feedback control law, 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. An a posteriori analysis proves, by deriving a piecewise-quadratic Lyapunov function, that the closed-loop system is exponentially stable. Simulation results demonstrate the potential advantages of the proposed control methodology.