On the perturbation of linear regular descriptor systems

Grigoris I. Kalogeropoulos, Athanasios D. Karageorgos, Athanasios A. Pantelous

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In the perturbation theory of linear descriptor systems, it is well known that the theory of eigenvalues and eigenvectors of regular homogeneous matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them to disappear. In this paper, the perturbation theory of complex Weierstrass canonical form for regular matrix pencils is investigated. Moreover, since there are applications such that the eigenvalues and eigenvectors do not disappear upon by arbitrarily small perturbations, expressions for the relative error of Fw and Gw, i.e., ∥ (F + E1)w - Fw ∥ / ∥ F w ∥ and ∥ (G + E2)w - Gw ∥ / ∥ Gw ∥ are provided by using the Frobenius norm ∥ ∥.

Original languageEnglish
Pages (from-to)5-13
Number of pages9
JournalSystems Science
Issue number4
Publication statusPublished - 2009
Externally publishedYes


  • Complex weierstrass canonical form
  • Linear systems
  • Perturbation theory

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