Bézout Identity in Pseudoratoinal Transfer Functions

Abstract

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