Region of attraction analysis via invariant sets

In this work we address the problem of estimating the region of attraction (RA) of a nonlinear dynamical system. We propose a method that uses a Lyapunov type approach to obtain an estimate of the RA, however, the obtained invariant sets are not level sets of the Lyapunov function certificates. We then restrict our attention to systems governed by polynomial vector fields and semi-algebraic sets and provide an algorithm that with each iteration is guaranteed to enlarge the estimate of the RA.