On generalized inverses of singular matrix pencils

Klaus Röbenack ; Kurt Reinschke

International Journal of Applied Mathematics and Computer Science, Tome 21 (2011), p. 161-172 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2011-01-01

Zbl 1221.93096

EUDML-ID : urn:eudml:doc:208031

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