A quadratic eigenproblem in the analysis of a time delay system
2006 (English)In: Proceedings in Applied Mathematics and Mechanics: PAMM, ISSN 1617-7061, E-ISSN 1617-7061, Vol. 6, no 1, 63-66 p.Article in journal (Refereed) Published
In this work we solve a quadratic eigenvalue problem occurring in a method to compute the set of delays of a linear time delay system (TDS) such that the system has an imaginary eigenvalue. The computationally dominating part of the method is to find all eigenvalues z of modulus one of the quadratic eigenvalue problem
Because of its origin in the vectorization of a Lyapunov type matrix equation, the quadratic eigenvalue problem is, even for moderate size problems, of very large size. We show one way to treat this problem by exploiting the Lyapunov type structure of the quadratic eigenvalue problem when constructing an iterative solver. More precisely, we show that the shift-invert operation for the companion form of the quadratic eigenvalue problem can be efficiently computed by solving a Sylvester equation. The usefulness of this exploitation is demonstrated with an example.
Place, publisher, year, edition, pages
2006. Vol. 6, no 1, 63-66 p.
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-53367DOI: 10.1002/pamm.200610017OAI: oai:DiVA.org:kth-53367DiVA: diva2:469996
GAMM Annual Meeting 2006. Berlin, Germany. March 27th - 31st 2006
QC 201205312011-12-272011-12-272012-05-31Bibliographically approved