An algebraic approach to delay differential systems

In this paper a class of delay differential systems is studied using an algebraic approach. Such a system is considered a system over a ring of delay operators. The ring under consideration is a valuation domain. This fact enables us to construct canonical free realizations and also regulators and observers. Algorithms in order to perform these constructions are given. The results are improvements upon the case where a delay differential system with incommensurable delays is viewed as a system over a polynomial ring in several variables.