Merrikh-Bayat Farshad, Karimi-Ghartemani Masoud
Sharif University of Technology, Tehran, Iran.
ISA Trans. 2009 Jan;48(1):32-7. doi: 10.1016/j.isatra.2008.10.003. Epub 2008 Nov 11.
This paper presents a numerical algorithm for BIBO stability testing of a certain class of the so-called fractional-delay systems. The characteristic function of the systems under consideration is a multi-valued function of the Laplace variable s which is defined on a Riemann surface with finite number of Riemann sheets where the origin is a branch point. The stability analysis of such systems is not straightforward because there is no universally applicable analytical method to find the roots of the characteristic equation on the right half-plane of the first Riemann sheet. The proposed method is based on the Rouche's theorem which provides the number of the zeros of a given function in a given simple closed contour. One advantage of the proposed method over previous works is that it gives the number and the location of the unstable poles. The algorithm has a reliable result which is illustrated by several examples.
本文提出了一种用于某类所谓分数延迟系统的有界输入有界输出（BIBO）稳定性测试的数值算法。所考虑系统的特征函数是拉普拉斯变量(s)的多值函数，它定义在具有有限个黎曼面的黎曼曲面上，其中原点是一个分支点。此类系统的稳定性分析并不直接，因为没有普遍适用的解析方法来找到第一黎曼面上右半平面中特征方程的根。所提出的方法基于儒歇定理，该定理给出了给定简单闭合轮廓内给定函数的零点个数。与先前工作相比，所提出方法的一个优点是它给出了不稳定极点的数量和位置。该算法具有可靠的结果，几个例子说明了这一点。
