中立型延时系统不稳定特征根的计算

摘要

提出了一种基于幅角原理计算一类中立型延时系统的所有不稳定特征根的算法.通过将右半复平面内的有界矩形区域或半圆形区域连续划分成较小的区域,能够有效地获得所有不稳定特征根的初始近似位置.以这些近似位置作为牛顿法的初始值,可迭代得到所有不稳定特征根的较好近似值.数值算例显示了算法的有效性.%We present an algorithm based on the argument principle for computing all unstable characteristic roots of a class of neutral time delay systems. By consecutively subdividing a bounded rectangular or half circular region on the right half complex plane into smaller ones, initial approximate positions of all unstable roots can be located efficiently and accurately. With these approximate positions as starting points for Newton's method, approximations for all roots are refined iteratively. The performance of the algorithm is shown by an example.