Relaxed periodic switching controllers of high-frequency DC-DC converters using the $\delta$ -operator formulation

This paper deals with the design of new periodic switching control laws for high frequency DC-DC converters. The contributions are twofolds. On a first hand, the DC-DC converter model is rewritten as a periodic switched affine system thanks to a $\delta$ -operator formulation, which represents an efficient framework for the numerical discretization at high frequencies. On a second hand, three different control laws are provided, the first one being the usual Lyapunov-based control law and the two others being relaxed versions of this first solution. The benefits of these two new control laws over the usual Lyapunov-based one are demonstrated on a simple example. More particularly, it is shown that the selection of the sampling period and of the control law strongly influence the size of the region of attraction.