Methods of Optimal Lyapunov Function Generation with Application to Power Electronic Converters and Systems

Stability is an important design consideration in power electronics systems. To this end, it is often of interest to predict the region of attraction (ROA) associated with a stable equilibrium point. In the case of the presence of constraints that need to be satisfied, one is faced with the problem of estimating a restricted ROA (RROA). Recently practical methods for estimating RROAs have been proposed for relatively high order systems. In this paper, a proposal is set forth for the problem of finding a Lyapunov function that yields an estimated restricted region of attraction that is close to the true restricted region of attraction. Numerical examples illustrate the proposed methods.