A novel technique for estimating the asymptotic stability region of nonlinear autonomous polynomial systems is established. The key idea consists of examining the optimal Lyapunov function (LF) level set that is fully included in a region satisfying the negative definiteness of its time derivative. The minor bound of the biggest achievable region, denoted as Largest Estimation Domain of Attraction (LEDA), can be calculated through a Generalised Eigenvalue Problem (GEVP) as a quasi-convex Linear Inequality Matrix (LMI) optimising approach. An iterative procedure is developed to attain the optimal volume or attraction region. Furthermore, a Chaotic Particular Swarm Optimisation (CPSO) efficient technique is suggested to compute the LF coefficients. The implementation of the established scheme was performed using the Matlab software environment. The synthesised methodology is evaluated throughout several benchmark examples and assessed with other results of peer technique in the literature.

中文翻译：

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混沌粒子群算法在多项式非线性系统中的吸引作用

建立了一种估计非线性自治多项式系统渐近稳定区域的新技术。关键思想包括检查最优Lyapunov函数（LF）水平集，该水平集完全包含在满足其时间导数的负定性的区域中。可以通过广义特征值问题（GEVP）作为准凸线性不等式矩阵（LMI）优化方法来计算最大可实现区域的最小界限，称为最大吸引力域（LEDA）。开发了一个迭代程序来获得最佳的体积或吸引区域。此外，提出了一种混沌特殊群优化（CPSO）高效技术来计算低频系数。建立的方案的实现是使用Matlab软件环境执行的。