Kronecker summation method and multiple delay systems

Ali Fuat Ergenc*, Nejat Olgac, Hassan Fazelinia

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A new procedure is presented for determining the kernel and the offspring hyperplanes for general LTI dynamics with multiple delays. These hyperplanes, as they are very recently introduced in a concept paper [1], form the basis of the overriding paradigm which is called the "Cluster Treatment of Characteristic Roots (CTCR)". In fact, these two sets of hyperplanes exhaustively represent the locations in the domain of the delays where the system possesses at least one pair of imaginary characteristic roots. To determine these kernel and offspring we use the extraordinary features of "Extended Kronecker Summation" operation in this paper. The end result is that the infinite dimensional problem reduces to a finite dimensional one (and preferably into an eigenvalue problem). Following the procedure described in this paper we are able to shorten the computational time considerably in determining these hyperplanes. We demonstrate these concepts via an example case study which treats a 3-delay system. For this case another perspective, called the "building block", is utilized to display the kernel in 3-D space of the "spectral delays".

Original languageEnglish
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1424401712, 9781424401710
Publication statusPublished - 2006
Externally publishedYes
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: 13 Dec 200615 Dec 2006

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference45th IEEE Conference on Decision and Control 2006, CDC
Country/TerritoryUnited States
CitySan Diego, CA


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