Computing optimal quadratic lyapunov functions for polynomial nonlinear systems via lmis

The problem of estimating the domain of attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities (LMIs) is proposed. Moreover, for the case of odd polynomial systems, a relaxed criterion for obtaining an effective starting candidate of the optimal quadratic Lyapunov function is presented.