A numerical algorithm for estimating the region of attraction of nonlinear systems with applications in power systems

This paper investigates estimating the region of attraction (ROA) of polynomial nonlinear systems. When the linearizing matrix of the nonlinear systems is critically stable, a shifting parameter is introduced. Using the weak quasi-one-sided Lipschitz condition, estimating the ROA of the systems is formulated by a global optimization problem. The homotopy method is applied to tackle the optimization problem globally. Finally, the presented algorithm is applied to analyze the stability of power systems.