Some Observations About the RMS Ring for Delayed Systems

This paper questions the validity of the definition and some properties of the RMS ring traditionally utilized for the description of time-delay systems. The original description of the ring is faced with findings obtained while dealing with this ring. In the light of these observations, it seems that a revisited definition of the ring ought to be formulated, and thus a new possible conception is presented in the contribution. It is also shown in the paper that the RMS ring proposed in the paper is not a unique factorization domain and thus it is not a principal ideal domain. The extended Euclidean algorithm is attempted to be performed for the ring to prove that it is a Bézout domain, which induces the question of existence of the coprime factorization for each pair of elements of the ring. These two problems are discussed; however, they remain partially unsolved.