![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
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.
ACKNOWLEDGMENT
Supported by research project DGESIC PB98-0753-C02-02.