Estimating the region of attraction based on a polynomial lyapunov function.

• Estimation of the regions of attraction using the quadratic Lyapunov functions is reported. • Recursive procedure for constructing a polynomial Lyapunov function is developed and described. • Effectiveness of the proposed approach is shown using various examples including systems with uncertain parameters. 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). [ABSTRACT FROM AUTHOR]