The classical buck converter is a very common DC–DC converter, which reduces an higher input supply voltage to a lower output load voltage. Replacing the inductor and the capacitor by a transmission line, we obtain a distributed buck converter, which can be described by partial differential equations. Therefore, we obtain a completely new class of model. This new topology can be used if the load is operated at some spatial distance from the power supply, where the power supply line is directly used as a reactive network element of the converter. In addition to the analysis and simulation we will also investigate the control of such a converter. In this contribution, we employ a discrepancy-based control technique. Approximating the theoretically derived feedback law yields an easy to implement sliding mode control scheme. The controller design is based on an ideal circuit model and verified by numerical simulation.