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Computation of subsets of the domain of attraction for polynomial systems

In this paper the asymptotic stability of polynomial nonlinear systems is investigated. Our aim is to determine a region in the state space, which is a subset of the domain of attraction. We use the Lyapunov stability theory and the theorem of Ehlich and Zeller to achieve this aim. The inequality conditions given by the theorem of Ehlich and Zeller enable us to calculate inner and outer approximations to the relevant region of attraction. Two nontrivial examples conclude the paper and show the effectiveness of the presented method.