Brunovsky's canonical form for linear dynamical systems over commutative rings

AbstractThis paper is devoted to studying the action of the feedback group on linear dynamical systems over a commutative ring R with unit. We characterize the class of m-input n-dimensional reachable linear dynamical systems ∑ = (F, G) over R that are feedback equivalent to a system ∑c = (Fc, Gc) with Brunovsky's canonical form. This characterization is obtained in terms of the minors of the matrices G̃∑i = (G, FG, …, Fi − 1G) for 1 ⩽i ⩽ n