On feedback invariants for linear dynamical systems Original Research Article

The goal of this paper is to prove that, if R is a commutative ring containing a (non-zero) finitely generated maximal ideal image containing its annihilator, such that every unit of image lifts to a unit of R, then the category of reachable systems over R is “wild” in the sense of classical representation theory. From this it follows that a canonical form for a reachable system over a PID is not likely to be found. More specifically, canonical forms are unlikely to be found for systems over image and k[T], when k is a field.