一种改进的吸引域估计的方法

An Improved Approach for Estimating Attraction Domain

在考察具有渐近稳定平衡点的非线性动力系统的时候,其吸引域范围是判断系统稳定性的一类重要指标.利用最优Lyapunovh函数法,可以得到一大类非线性动力系统所对应的Lyapunov函数,并利用该函数对吸引域范围进行估计.基于最优最优Lyapunov函数,通过对原吸引域估计方法进行改进,可以显著提高估计的准确性,得到更好估计结果,并通过数值实验证明了这一点。

When investigating the property of nonlinear dynamical system which has asymptotically equilibrium point,the range of its corresponding attractive domain is an important indicator for system stability.By using optimal Lyapunov function approach,the corresponding Lyapunov function can be obtained for large part of nonlinear dynamical systems,which can be used to estimate the range of attraction domain.On basis of optimal Lyapunov function,the original approach for estimating attraction is improved,which effectively increases the estimating accuracy to obtain better estimating result.Numerical Examples are given to show this.