The Lambert W function and the spectrum of some multidimensional time-delay systems

被引：53
|
作者：
Jarlebring, Elias [1 ]
Damm, Tobias [2 ]
机构：
[1] Tech Univ Carolo Wilhelmina Braunschweig, Inst Computat Math, D-38023 Braunschweig, Germany
[2] TU Kaiserslautern, Technomath Grp, D-67653 Kaiserslautern, Germany
来源：
AUTOMATICA | 2007年 / 43卷 / 12期
关键词：
Lambert W function; linear time-delay systems; simultaneous triangularization; matrix function; Jordan canonical form;
D O I：
10.1016/j.automatica.2007.04.001
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this note we find an explicit expression for the eigenvalues of a retarded time-delay system with one delay, for the special case that the system matrices are simultaneously triangularizable, which includes the case where they commute. Using matrix function definitions we define a matrix version of the Lambert W function, from which we form the expression. We prove by counter-example that some expressions in other publications on Lambert W for time-delay systems do not always hold. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2124 / 2128
页数：5
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