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The Lambert W function and the spectrum of some multidimensional time-delay systems
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.ORCID iD: 0000-0001-9443-8772
2007 (English)In: Automatica, ISSN 0005-1098, Vol. 43, no 12, 2124-2128 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 43, no 12, 2124-2128 p.
Keyword [en]
Lambert W function; linear time-delay systems; simultaneous triangularization; matrix function; Jordan canonical form
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-53252DOI: 10.1016/j.automatica.2007.04.001ISI: 000251813100015OAI: diva2:469688
QC 20120219Available from: 2011-12-26 Created: 2011-12-26 Last updated: 2012-02-19Bibliographically approved

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Jarlebring, Elias
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