On Critical Delays for Linear Neutral Delay Systems
2007 (English)In: Proceedings of the European Control Conference, 2007Conference paper (Refereed)
In this work we address the problem of finding the critical delays of a linear neutral delay system, i.e., the delays such that the system has a purely imaginary eigenvalue. Even though neutral delay systems exhibit some discontinuity properties with respect to changes in the delays an essential part in a non-conservative stability analysis with respect to changes in the delays, is the computation of the critical delays. We generalize previous results on critical delays and stability switches for retarded time-delay systems, under some minor assumptions on the delay system. The work starts with stating a general equivalence theorem between the spectrum and a matrix function condition.We show how this theorem can be applied to the commensurate timedelay system to compute the critical delays. It turns out that the resulting method is closely related to parts of the results of Fu, Niculescu and Chen. For the incommensurate case we present a scheme which allows the computation of the critical curves, i.e., the points in delay-space for which the system has a purely imaginary eigenvalue. We apply the method to previously investigated examples, in order to provide a verification of the results, as well as to an example for which the stability picture is, to our knowledge, not yet known.
Place, publisher, year, edition, pages
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-53370OAI: oai:DiVA.org:kth-53370DiVA: diva2:469999
European Control Conference, Kos, Greece, 2-5 July 2007
QC 201202062011-12-272011-12-272012-02-06Bibliographically approved