Multiple Lyapunov function based reaching condition for orbital existence of switching power converters

A methodology to analyze the reaching condition of a switching power converter (SPC) using Lyapunov's direct method and a piecewise linear model is outlined. By using a multiple Lyapunov function, the reaching criteria for orbital existence of a SPC is formulated as a linear matrix inequality that is solved using a convex optimization solver. Further, the criterion is modified to distinguish the different modes (i.e., sliding and asymptotic modes and combination of the two fundamental modes) of convergences of the reaching dynamics. The applicability of the reaching criteria for solving practical problems using case illustrations of dc-dc converters and three-phase dc-ac converters operating with different control and modulation techniques is demonstrated. The methodology developed in this paper can be potentially extended to other SPCs and may lead to the development of optimal-sequence control techniques that can dynamically change the mode and the rate of convergence of a SPC.