Abstract
ABSTRACT In this paper we study the action of the feedback group on m-input, 2-dimensional linear dynamical systems over a commutative ring R, in order to calculate canonical forms. We define a set for each element g of R . For a class of systems, a complete set of canonical forms can be constructed associated with pairs , where f belongs to . If the ring is an elementary divisor domain, in particular a P.I.D., this method applies to all reachable systems. When R is a Dedekind domain, a formula is obtained for calculating using the factorization of gR in powers of prime ideals. We also establish two conditions on the ring which imply that each set , is finite. For the rings and , we calculate explicitely the canonical forms, improving by this way the known results about the number of feedback classes over these rings. Finally, effective calculations are made when R is the ring of integers of an algebraic field, using methods of Computational Algebra.
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