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Mathematica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。
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.
出处
《动力学与控制学报》
2009年第2期136-142,共7页
Journal of Dynamics and Control
基金
国家杰出青年科学基金项目(10825207)
国家自然科学基金重点项目(10532050)
全国优秀博士学位论文作者专项基金项目资助~~
