A convolution algebra of delay-differential operators and a related problem of finite spectrum assignability

In this paper we investigate a ring of delay-differential operators, which appears in the study of time-delay systems with commensurate point delays. Besides point-delay differential operators, this ring also contains certain distributed delays. It can be described as a certain algebraic extension of the ring of point-delay differential operators as well as a convolution algebra of compact support distributions. It will be shown that the finite spectrum assignability problem can be solved for spectrally controllable systems with controllers from this algebra.