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Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
- Source :
-
Linear Algebra & its Applications . Jul2009, Vol. 431 Issue 3/4, p369-380. 12p. - Publication Year :
- 2009
-
Abstract
- Abstract: 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 431
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 39785154
- Full Text :
- https://doi.org/10.1016/j.laa.2009.02.008