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Abstract: For nonnecessarily reachable systems over a commutative ring R, we define a strong form of feedback cyclization (FC). With this natural generalization of the FC property we obtain a feedback reduced form for systems over strong FC rings (i.e. rings for which every system verifies the FC property). In the particular case of reachable single input systems, this gives the usual control canonical form of Bumby et al. [Remarks on the pole-shifting problem over rings, J. Pure Appl. Algebra 20 (1981) 113–127]. Also it is proved that a commutative ring with 1 in its stable range has the strong FC property if and only if it has the UCU property, which is the natural parallel form of the result given by Brewer et al. [Pole assignability in polynomial rings, power series rings and Prüfer domains, J. Algebra 106 (1987) 265–286] for the reachable case. Many classes of rings which were known to be FC rings are in fact strong FC rings, but there are FC rings which are not strong FC rings. [Copyright &y& Elsevier]

If ( A , B ) is a finite system over a commutative von Neumann regular ring R , the problem of searching for a matrix F such that the pencil [ s I − A − B F ] has some prescribed Smith normal form is reduced to the case where R is a field, a problem which for controllable systems is described by a well-known theorem of Rosenbrock on pole assignment [12] , and was then generalized to noncontrollable pairs [14] . It this paper, von Neumann regular rings are characterized as the class of commutative rings for which the solution of the above problem over the ring is equivalent to its solution in each residue field. [ABSTRACT FROM AUTHOR]