Kernel-representations and realizations of delay-differential systems

We investigate linear time-invariant delay-differential systems within the behavioral approach. A suitable ring of operators including polynomial delay-differential operators with commensurate point-delays but also some specific distributed delay operators is introduced. Within this class of operators it is shown that ARMA-systems do always admit a kernel-representation. Furthermore, we characterize those operator matrices, which are realizable as a first-order system. In this case, the polynomial model of Fuhrmann is shown to be a realization in the behavioral sense.