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

页码：2124 / 2128

页数：5

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