1. E.D. Sontag. On the internal realization of nonlinear behaviors. In A. Bednarek and L. Cesari, editors, Dynamical Systems, pages 93-497. Academic Press, New York, 1977.



2. E.D. Sontag. The lattice of minimal realizations of response maps over rings. Math. Systems Theory, 11(2):169-175, 1977. [PDF] Keyword(s): systems over rings, parametric classes of systems. Abstract:

   A lattice characterization is given for the class of minimal-rank realizations of a linear response map defined over a (commutative) Noetherian integral domain. As a corollary, it is proved that there are only finitely many nonisomorphic minimal-rank realizations of a response map over the integers, while for delay -differential systems these are classified by a lattice of subspaces of a finite-dimensional real vector space.




3. E.D. Sontag and Y. Rouchaleau. Sur les anneaux de Fatou forts. C. R. Acad. Sci. Paris Sér. A-B, 284(5):A331-A333, 1977. [PDF] Keyword(s): systems over rings, parametric classes of systems. Abstract:

   It is well known that principal rings are strong Fatou rings. We construct here a more general type of strong Fatou rings. We also prove that the monoid of divisor classes of a noetherian strong Fatou ring contains only the zero element, and that the dimension of such a ring is at most two.

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