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Feedback classification of linear systems over von Neumann regular rings

By Andres Saez-Schwedt and Wiland Schmale


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.Comment: 10 page

Topics: Mathematics - Dynamical Systems, Mathematics - Commutative Algebra, 93B25
Year: 2011
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