Canonical forms for linear dynamical systems over commutative rings: The local case (Q2738448)

The authors survey some results on the Brunovsky canonical form for the feedback equivalence of reachable linear dynamical systems over commutative rings. Besides the general definition and well-known facts, they include some very recent results: A normal form for reachable linear dynamical systems over a local ring \(R\) is given. This normal form is a canonical form in the case of two-dimensional systems. Finally, the case of a discrete valuation domain \(R\) is specially treated: They obtain a complete set of invariants and a canonical form for a reachable \(n\)-dimensional linear dynamical system \(\Sigma\) with the property that the invariant \(R\)-modules \(M^{\Sigma}_1, M^{\Sigma}_2, \ldots, M^{\Sigma}_n\) are free except at most one of them.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00025].