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Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations

Please always quote using this URN:urn:nbn:de:0296-matheon-13222
  • An eigenvalue perturbation theory under rank-one perturbations is developed for classes of real matrices that are symmetric with respect to a non-degenerate bilinear form, or Hamiltonian with respect to a non-degenerate skew-symmetric form. In contrast to the case of complex matrices, the sign characteristic is a crucial feature of matrices in these classes. The behavior of the sign characteristic under generic rank-one perturbations is analyzed in each of these two classes of matrices. Partial results are presented, but some questions remain open. Applications include boundedness and robust boundedness for solutions of structured systems of linear differential equations with respect to general perturbations as well as with respect to structured rank perturbations of the coefficients.

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Metadaten
Author:Christian Mehl, Volker Mehrmann, Andre Ran, Leiba Rodman
URN:urn:nbn:de:0296-matheon-13222
Referee:Caren Tischendorf
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/08/27
Release Date:2014/08/27
Institute:Technische Universität Berlin
Project:C Energy and Materials (Production) / C-SE3 Stability analysis of power networks and power network models
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx]
Preprint Number:1071
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