Unimodular Transformations and Canonical Forms for Singular Systems

Abstract

The relationship between the unimodular matrices relating coprime and column reduced matrix fraction descriptions (MFD) of a nonproper transfer function, and the restricted system equivalence (r.s.e.) transformations relating the corresponding generalised state space realisations is considered. It is shown that the r.s.e and unimodular transformations can be directly obtained from each other by inspection. The r.s.e. transformations leading to the canonical form are derived from the unimodular transformations leading to the echelon canonical form of the composite matrix of the MFD of the system.