Bézout Identity in Pseudoratoinal Transfer Functions

Coprime factorizations of transfer functions play various important roles, e.g., minimality realizations, stabilizability systems, etc. This paper studies the Bézout condition over ring E′(ℝ_) distributions compact support and M(ℝ_) measures with support. These spaces are known to crucial roles in state space representations controllability behaviors. We give a detailed review results obtained thus far, as well discussions on new attempt deriving general from that for measures. It is clarified there technical gap generalizing result E′(ℝ_). A study concrete example given.