This paper deals with the stabilization of high frequency DC-DC converters. This kind of systems can be modeled as switched affine systems subject to a periodic sampled-data control implementation. The dynamics of these systems is expressed using the δ-operator in order to cope with high frequency switching control constraints. The novelties of this paper, first, relies on the formulation of a freematrices based min-projection control law, that allows the selection of the mode to be activated,

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... ased on the knowledge of the state variables. Second, the stability theorem, expressed in terms of a tractable optimization problem, that guarantees a practical stability result to a set and delivers the optimal control law that minimizes the volume of this one. The method is then illustrated through the control of a high frequency boost converter.