A structural approach for computing stability domains of polynomial systems

The problem of estimating the stability domain of the origin of an n-order polynomial system containing linear, quadratic and cubic terms is considered. Exploiting the structure of this class of systems, it is shown that for a given quadratic Lyapunov function an estimate of the stability domain can be obtained by solving a suitable optimization problem which has the distinguished feature of being convex. The accuracy of the proposed method and its possible use in the available numerical procedures for estimating the stability domain are discussed via several examples