Estimating the region of attraction based on a polynomial lyapunov function

摘要

This paper deals with the problem of obtaining estimates of the domains of attraction and stability in nonlinear dynamical systems. It is based on a special recursive procedure for constructing polynomial Lyapunov functions. The procedure is tested on several examples used in previous studies by other authors, with a comparison of the results. The approach is also applied to estimate the domain of attraction for single DoF mechanical systems with uncertain parameters (Van der Pol and Duffing oscillators).