On generalized inverses of singular matrix pencils

Authors:
Klaus RöBenack;Kurt Reinschke
Affiliations:
Institute of Control Theory Faculty of Electrical and Computer Engineering, Technische Universität Dresden, D-01062 Dresden, Germany;Institute of Control Theory Faculty of Electrical and Computer Engineering, Technische Universität Dresden, D-01062 Dresden, Germany
Venue:
International Journal of Applied Mathematics and Computer Science - Semantic Knowledge Engineering
Year:
2011

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Abstract

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.