Exact Region of Attraction Determination Based on Manifold Method

The exact region of attraction plays an important role in autonomous nonlinear system, while the results based on the conventional method, such as Lyapunov function approach, are always conservative. However, results via the manifold method, which is the main approach studied, are exact. This method optimizes the distribution of points on the circle through modifying the end point of the former trajectory and inserting/deleting point on the circle on the basis of trajectory arc length method to improve the accuracy and efficiency. First, the basic theory of manifold method is introduced. Secondly, a methodology for determining stable manifold are proposed, which is the core of the manifold method in stability boundary determining. Finally, on this basis, three examples about academic model, power system and aviation system are taken to illustrate the advantages of the method. The results show that the method can improve the accuracy and significantly reduce the calculation time, and can be widely used in engineering systems.