一类时滞系统Hurwitz稳定的简单判据
李俊余，王在华
摘要: 近年来,Lambert w函数已被成功的应用到时滞系统的稳定性分析中. 但由于Lambert W函数是一个超越方程的解, 而且它的求解需要借助数学软件Maple, Matlab或Matllematica才能完成, 因此在理解和应用. 上都有一定困难. 本文通过深入研究, 首先利用初等函数描述了Lambert W函数根的分布情况, 进而给出了一类时滞系统渐近稳定和鲁棒稳定的简单判据. 利用新的判据, 原来可以用Lambert W函数来判定的时滞系统的稳定性问题, 现在只需要用初等函数就可以解决.
关键词：Lainbert W 函数；稳定性；时滞系统；鲁棒稳定性
Simple criteria for the Hurwitz stability of some time - delay systems
Junyu Li, Zaihua Wang
Abstract：Recently, Lambert W function has been found successful applications in stability analysis of time - delay systems. Because Lambert W function is defined as the solution of a transcendental equation, and it works only if some mathematical softwares such as Maple, Matlab or Mathematica are available, so the stability criteria based on Lambert W functions are not easy for understanding in applications. In this paper, two simple stability criteria have been derived from a careful investigation of the root location of Lambert W function, so that the stability as well as the robust stability of some time - delay systems checked by using Lambert W function can now be tested simply by calculating elementary functions.
Keyword：Lambert W function; stability; time -delay system; robust stability
原文链接：http://dlxykzxb.cnjournals.net/jdc/article/abstract/20090208?st=search
