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An analytical method of estimating the domain of attraction forpolynomial differential equations

机译：多项式微分方程吸引域估计的一种解析方法

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摘要

A system of nth-order differential equations with polynomial right-hand sides is considered, and a simple analytical method of estimating the domain of attraction is developed. The method involves an ordinary quadratic Lyapunov function υ=XTQ(Y)X with a certain parameter vector Y from the same state space. All linear factors in the expression for υ˙ are bounded in the domain υ⩽1, and the derivative is bounded by a quadratic function, the negativeness of which determines the restrictions for Y. The domain of attraction is estimated through a simple scaling of the obtained area or through its nonlinear transformation with optimization. The method allows for obtaining domains (for example, with infinite volume) that are comparable with ones obtained by complicated computational procedures. A set of examples is presented
机译：考虑具有多项式右侧的n阶微分方程系统，并开发了一种简单的吸引域估计分析方法。该方法包括具有来自相同状态空间的特定参数向量Y的普通二次Lyapunov函数＝ XTQ（Y）X。表达式中的所有线性因子限制在域＆les; 1中，导数由二次函数界定，二次函数的负性确定对Y的限制。吸引域通过简单缩放获得的面积或通过其非线性变换来估算优化。该方法允许获得与通过复杂的计算过程获得的域可比的域（例如，无限大的域）。提出了一组例子

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