Estimation of the domain of attraction for non-polynomial systems: A novel method

Until now, several methods have been developed to compute the domains of attraction for stationary points of polynomial non-linear systems. For the case of non-polynomial systems, though, this question is still open. In this paper a new method, based on Lyapunov’s stability theory and the theorem of Ehlich and Zeller, is presented for the computation of domains of attraction of non-polynomial systems with quadratic Lyapunov functions. Unlike other methods, which use a polynomial approximation for the non-polynomial terms, we compute upper bounds on the interpolation error for each of the non-polynomial terms. Then, the theorem of Ehlich and Zeller is adapted to non-polynomial systems. Our method yields, for a given Lyapunov function, upper and lower bounds for the level curve enclosing the domain of attraction.