Estimating the domain of attraction: a light LMI technique for a class of polynomial systems

The problem of computing the largest estimate of the domain of attraction (LEDA) of an equilibrium point for a given Lyapunov function is considered for a class of polynomial systems described by a linear and a homogeneous polynomial term. Such a class contains well known examples in control theory as the prey-predatory system, mass-spring systems with softening/hardening springs and electric circuits with vacuum tubes. It is shown that a lower bound of the LEDA can be obtained through a convex optimization constrained by a linear matrix inequality (LMI). The contribution of the proposed technique with respect to the existing approaches consists of requiring a significantly smaller computational burden and guaranteeing the lower bound tightness for some system dimensions and degrees.