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Paper details
Number 1 - March 2011
Volume 21 - 2011
On generalized inverses of singular matrix pencils
Klaus Röbenack, Kurt Reinschke
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.
Keywords
matrix pencils, Kronecker indices, Moore–Penrose inverse, Drazin inverse, linear networks