Feedback invariants for linear dynamical systems over a principal ideal domain Original Research Article

This paper studies the action of the feedback group Fn,m on m-input, n-dimensional reachable linear dynamical systems over a principal ideal domain R. For such a 2-dimensional system ∑ a complete set of invariants is given which characterizes the feedback class of ∑. In particular it is characterized, in terms of these invariants, when ∑ has the feedback cyclization property. The particular cases R = Z and R = R[X] are studied in some detail. Finally, when n is arbitrary, the feedback classification is given for the class of reachable systems ∑ = (F, G) such that G is a matrix with at least n − 1 invariant factors equal to one.