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.
李俊余,王在华.一类时滞系统Hurwitz稳定的简单判据[J].动力学与控制学报,2009,7(2):136~142; Li Junyu, Wang Zaihua. Simple criteria for the hurwitz stability of some time-delay systems[J]. Journal of Dynamics and Control,2009,7(2):136-142.
