Optimal State-Feedback Control of Bilinear DC–DC Converters With Guaranteed Regions of Stability

This paper deals with the modeling and the robust controller synthesis for nonlinear dc-dc converters. In the first part of this paper, a model for the bilinear dynamics is presented. Such nonlinear dynamics can be included in a convex polytope such that the trajectories of the converter out of the equilibrium are assured to remain inside a guaranteed region of stability despite of the bilinear term. Such a description of the dynamic response of the converter is employed, in the second part of this paper, to propose synthesis algorithms that can guarantee, a priori, the stability and performance requirements of the design. The resulting region of stability can take into account not only the bilinear terms but also the saturation of the control input, which is a topic of major importance in high-performance dc-dc converters. The aim of this paper is to contribute with a robust control framework which allows the designers to deal with the common requirements of regulated dc-dc converters. The correctness of the results has been verified both with numerical simulations and experimental measurements from dc-dc converter prototypes.