Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations

E. Jarlebring, M.E. Hochstenbach

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

31 Citaten (Scopus)

Samenvatting

Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called matrix pencil methods, the general ideas used as well as the proofs differ considerably. Moreover, the available theory hardly reveals the relations between the different methods. In this work, a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem: the polynomial two-parameter eigenvalue problem, of which the quadratic two-parameter eigenvalue problem is a special case. This framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods. We also recognize a few new matrix pencil variants to determine DDE stability. Finally, the recognition of the new types of eigenvalue problem opens a door to efficient computation of DDE stability.
Originele taal-2Engels
Pagina's (van-tot)369-380
TijdschriftLinear Algebra and Its Applications
Volume431
Nummer van het tijdschrift3-4
DOI's
StatusGepubliceerd - 2009

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