The Lambert W function and the spectrum of some multidimensional time-delay systems
2007 (English)In: Automatica, ISSN 0005-1098, Vol. 43, no 12, 2124-2128 p.Article in journal (Refereed) Published
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.
Lambert W function; linear time-delay systems; simultaneous triangularization; matrix function; Jordan canonical form
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-53252DOI: 10.1016/j.automatica.2007.04.001ISI: 000251813100015OAI: oai:DiVA.org:kth-53252DiVA: diva2:469688
QC 201202192011-12-262011-12-262012-02-19Bibliographically approved