1. E.D. Sontag and Y. Yamamoto. On the existence of approximately coprime factorizations for retarded systems. Systems Control Lett., 13(1):53-58, 1989. [PDF] [doi:http://dx.doi.org/10.1016/0167-6911(89)90020-0] Keyword(s): delay-differential systems. Abstract:

   This note establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distributions. The latter have been employed by the second author in the study of function-space controllability for such systems.




2. Y. Rouchaleau and E.D. Sontag. On the existence of minimal realizations of linear dynamical systems over Noetherian integral domains. J. Comput. System Sci., 18(1):65-75, 1979. [PDF] Keyword(s): systems over rings. Abstract:

   This paper studies the problem of obtaining minimal realizations of linear input/output maps defined over rings. In particular, it is shown that, contrary to the case of systems over fields, it is in general impossible to obtain realizations whose dimiension equals the rank of the Hankel matrix. A characterization is given of those (Noetherian) rings over which realizations of such dimensions can he always obtained, and the result is applied to delay-differential systems.




3. E.D. Sontag. On finitary linear systems. Kybernetika (Prague), 15(5):349-358, 1979. [PDF] Keyword(s): systems over rings. Abstract:

   An abstract operator approach is introduced, permitting a unified study of discrete- and continuous-time linear control systems. As an application, an algorithm is given for deciding if a linear system can be built from any fixed set of linear components. Finally, a criterion is given for reachability of the abstract systems introduced, giving thus a unified proof of known reachability results for discrete-time, continuous-time, and delay-differential systems.




4. E.D. Sontag. On split realizations of response maps over rings. Information and Control, 37(1):23-33, 1978. [PDF] Keyword(s): systems over rings. Abstract:

   This paper deals with observability properties of realizations of linear response maps defined over commutative rings. A characterization is given for those maps which admit realizations which are simultaneously reachable and observable in a strong sense. Applications are given to delay-differential systems.

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