2011/03/05 by Andres Saez-Schwedt, Saez-Schwedt, Andres, Wiland Schmale +1
Mathematics · #93B25 #Commutative Algebra (math.AC) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AC #math.DS #msc:93B25
paper · pdf · doi:10.48550/arxiv.1103.1018
10 pages
arxiv created 2011/03/05 · arxiv updated 2011/03/08
It is proved that feedback classification of a linear system over a commutative von Neumann regular ring R can be reduced to the classification of a finite family of systems, each of which is properly split into a reachable and a non-reachable part, where the reachable part is in a Brunovski-type canonical form, while the non-reachable part can only be altered by similarity. If a canonical form is known for similarity of matrices over R, then it can be used to construct a canonical form for feedback equivalence. An explicit algorithm is given to obtain the canonical form in a computable context together with an example over a finite ring.