This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.

中文翻译：

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基于Lyapunov的吸引域最大化方法

本文研究了Lyapunov方法来扩展非线性自治模型的吸引域（DA）。已经对这些技术进行了研究，以创建以有理和二次Lyapunov函数为中心的通用数值程序。结果来自所有研究的方法：通过阈值接受算法（TAA）进行估算的方法，通过Zubov技术进行估算的方法以及通过线性矩阵不等式（LMI）优化和遗传算法（GA）进行的估算方法。这些方法对于大量的非线性模型是有效的，它们具有显着的改善吸引域面积的能力，并且它们的明显特征是直接适用于高度紧凑的非线性模型。基于模拟案例分析确定了所检查技术的有效性和有效性。通过研究著名的Van der Pol模型来评估和讨论所提出方法的有效性。