Feedback invariants for linear systems defined over rings

In this paper, we present a coefficient-assignability theorem for systems defined over a commutative ring with 1. While examples show that the hypothesis is not a necessary condition, the recent counterexample given by Bumby and Sontag [5] shows that some hypothesis is required and the conditions given here do include, as special cases, all the general results (of which the author is aware) about coefficient-assignability previously discovered. It should be remarked, however, that if we restrict our attention to the weaker property of pole-placement and assume that R is a P.I.D., then our techniques gain no new leverage and, although it does not include our result, the well-known theorem of A.S. Morse [10] still seems to be the best result available in this situation.