NDLI: Kronecker Summation Method and Multiple Delay Systems

Content Provider	IEEE Xplore Digital Library
Author	Ergenc, A.F. Olgac, N. Fazelinia, H.
Copyright Year	2006
Description	Author affiliation: Connecticut Univ. (Ergenc, A.F.; Olgac, N.; Fazelinia, H.)
Abstract	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 (Sipahi and Olgae, 2005), 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 3D space of the "spectral delays"
Starting Page	4417
Ending Page	4422
File Size	6969904
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377120
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Delay systems Kernel Robust stability Delay effects Polynomials Uncertainty Equations Control systems USA Councils Eigenvalues and eigenfunctions
Content Type	Text
Resource Type	Article

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