Multiple Lyapunov function based reaching condition analyses of switching power converters

We present a technique to analyze the period-1 reaching conditions of power electronics systems (PESs) using multiple Lyapunov functions. A piecewise linear model of the PES is used, which can accurately analyze a wide range of PES dynamics because of its close resemblance to the actual system. By formulating a convex optimization problem based on a composite Lyapunov function and solving this problem using well-known numerical algorithms, we predict the reaching conditions of the PES. The analyses techniques presented in this paper can be used to predict whether the converter dynamics approach a switching surface or not during transient/start-up conditions.