Control of bilinear power converters using sum of squares programming

In this paper, stabilization of a class of power converters with discrete-time bilinear averaged dynamic model is investigated by using Sum of Squares (SOS) programming and quadratic Lyapunov functions. A general bilinear mathematical discrete model is derived for a class of DC/DC power converters and the coordinates of the developed model are transformed to the origin. A controller design methodology based on SOS programming that has been developed in previous works is applied to various power converter models. The controller design allows for maximizing the region of convergence, and/or guaranteeing a certain exponential rate of decay, while input constraints are fulfilled. The resulting controller designs are evaluated using detailed switching models, and are shown to compare favorably with controller designs available in literature.