Estimation of the domain of attraction for polynomial systems

In this paper the asymptotic stability of polynomial nonlinear systems is investigated. Our goal is, based upon modern results of real algebraic geometry, to compute subsets of the region of attraction of asymptotically stable stationary points of polynomial systems. A theorem of Toeplitz and the Lyapunov stability theory are applied to achieve the aim. Especially the inequality conditions given by the theorem of Toeplitz enable the calculation of the inner approximation to the relevant region of the domain of attraction. An instructive example is discussed to show the results of the presented approach.