Abstract
This 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 = ( F c , G c ) with Brunovsky's canonical form. This characterization is obtained in terms of the minors of the matrices G ̃ ∑ i = (G, FG, …, F i − 1G) for 1 ⩽i ⩽ n .
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