Coprime factorization of singular linear systems. A Stein matritial equation approach

Abstract

In this work immersed in the eld of control theory on a Given a singular linear dynamic time invariant represented by Ex + ( t ) = Ax ( t ) Bu ( t ), y ( t ) = Cx ( t ). We want to classify singular systems such that by means a feedback and an output injection, the transfer ma- trix of the system is a polynomial, for that we analyze conditions for obtention of a coprime factorization of transfer matrices of singular lin- ear systems de ned over commutative rings R with element unit. The problem presented is related to the existence of solutions of a Stein matritial equation XE NXA = Z .