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

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• 作者：Elias Jarlebring ; Tobias Damm
• 关键词：Lambert W function ; Linear time-delay systems ; Simultaneous triangularization ; Matrix function ; Jordan canonical form
• 刊名：Automatica
• 出版年：2007
• 期刊代码：13_00051098
• 类别：cp
• 出版时间：December 2007
• 卷：43
• 期：12
• 页码：2124-2128
• 文件大小：158 K

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 the MathML source">W function, from which we form the expression. We prove by counter-example that some expressions in other publications on Lambert w the MathML source">W for time-delay systems do not always hold.