When an isolated equilibrium of a nonlinear system is locally attractive, it might be difficult to estimate and then enlarge its Region of Attraction (RA). To solve this problem, this paper, by means of impulsive control, provides an effective method, i.e., state-dependent edge impulse (STDEI) combining with SOS programming and trajectory reversing with convex hull. Based on SOS programming and trajectory reversing, the initial estimation of RA is established. Then, by applying STDEI, we can design and then obtain the enlarged estimation of RA. Three numerical examples are provided to demonstrate the performance of the proposed approaches.

中文翻译：

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通过状态相关的边缘脉冲来估计和扩大多平衡点系统的吸引区域

当非线性系统的孤立平衡局部有吸引力时，可能难以估计然后扩大其吸引力区域（RA）。为了解决这个问题，本文通过脉冲控制的方法，提出了一种有效的方法，即状态依赖的边缘脉冲（STDEI）与SOS编程以及凸壳的轨迹反转相结合。基于SOS编程和轨迹反转，建立了RA的初始估计。然后，通过应用STDEI，我们可以设计然后获得RA的扩大估计。提供了三个数值示例来演示所提出方法的性能。