On generalized inverses of singular matrix pencils

Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass struct...

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Bibliographic Details
Published inInternational Journal of Applied Mathematics and Computer Science Vol. 21; no. 1; pp. 161 - 172
Main Authors Röbenack, Klaus, Reinschke, Kurt
Format Journal Article
LanguageEnglish
Published Zielona Góra Versita 01.03.2011
De Gruyter Poland
Subjects
Circuits
Computer simulation
Drazin inverse
Inverse
Kronecker indices
linear networks
Mathematical analysis
Mathematical models
matrix pencils
Moore-Penrose inverse
Networks
Pencils
Poles
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Summary:Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the multiplicity of poles at zero of the Moore-Penrose inverse and the Drazin inverse of the rational matrix are investigated. We present example networks whose circuit equations yield singular matrix pencils.
Bibliography:ark:/67375/QT4-L6KSVLJK-0
ArticleID:v10006-011-0012-3
istex:13737060EBB6837A08A3CB16BCAFE4737E5AEAA3
v10006-011-0012-3.pdf
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ISSN:1641-876X
2083-8492
DOI:10.2478/v10006-011-0012-3