Feedback classification of linear systems over von Neumann regular rings

Details Feedback classification of linear systems over von Neumann regular rings Feedback classification of linear systems over von Neumann regular rings

2011-03-05

arxiv.org/abs/1103.1018v1

Mathematics

Dynamical Systems

10 pages

Scientific paper

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.

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