1. E.D. Sontag. On the internal realization of polynomial response maps. PhD thesis, Univ. of Florida, Advisor: R.E. Kalman, 1976.

1. E.D. Sontag. Linear systems over commutative rings: A survey. Ricerche di Automatica, 7:1-34, 1976. [PDF] Keyword(s): systems over rings, parametric classes of systems. Abstract:

   An elementary presentation is given of some of the main motivations and known results on linear systems over rings, including questions of realization and control. The analogies and differences with the more standard case of systems over fields are emphasized throughout.




2. E.D. Sontag. On finitely accessible and finitely observable rings. J. Pure Appl. Algebra, 8(1):97-104, 1976. [PDF] Keyword(s): systems over rings, parametric classes of systems, observability, noncommutative rings. Abstract:

   Two classes of rings which occur in linear system theory are introduced and compared. Characterizations of one of them are given in terms, of integral extensions (every finite extension of R is integral) and Cayley--Hamilton type matrix condition. A comparison is made in the case of no zero-divisors with Ore domains.




3. E.D. Sontag and Y. Rouchaleau. On discrete-time polynomial systems. Nonlinear Anal., 1(1):55-64, 1976. [PDF] Keyword(s): identifiability, observability, polynomial systems, realization theory, discrete-time. Abstract:

   Considered here are a type of discrete-time systems which have algebraic constraints on their state set and for which the state transitions are given by (arbitrary) polynomial functions of the inputs and state variables. The paper studies reachability in bounded time, the problem of deciding whether two systems have the same external behavior by applying finitely many inputs, the fact that finitely many inputs (which can be chosen quite arbitrarily) are sufficient to separate those states of a system which are distinguishable, and introduces the subject of realization theory for this class of systems.

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