1. 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.




2. E.D. Sontag. On linear systems and noncommutative rings. Math. Systems Theory, 9(4):327-344, 1975. [PDF] Keyword(s): systems over rings, parametric classes of systems. Abstract:

   This paper studies some problems appearing in the extension of the theory of linear dynamical systems to the case in which parameters are taken from noncommutative rings. Purely algebraic statements of some of the problems are also obtained. Through systems defined by operator rings, the theory of linear systems over rings may be applied to other areas of automata and control theory; several such applications are outlined.

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