COPRIME FACTORIZATION OF THE TRANSFER MATRIX OF A SINGULAR LINEAR SYSTEM
M. Isabel Garcia-Planas, Montserrat Lopez-Cabeceira
Given a linear dynamic time invariant
represented by $x^{+}(t) = Ax(t) Bu(t)$, $y(t)=Cx(t)$, we analyze conditions for obtention of a coprime factorization of transfer matrices of singular linear systems defined over commutative rings $R$ with element unit.
The problem presented is related to the existence of solutions of a matrix equation
$XE- NXA = Z $.