Publications by Eduardo D. Sontag in year 1977
Articles in journal or book chapters
  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.
    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 SÚr. A-B, 284(5):A331-A333, 1977. [PDF] Keyword(s): systems over rings.
    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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