Abstract
Abstract The formal reachability property for a pair of matrices (A, B) over the polynomial ring ℛ = R[d1..., dk] in k symbols with real coefficients is considered where A is n by n, B is n by m with integers m being fixed. Reachability is defined as the property that ImRscr;[A|B]= ℛn n where [A |B] = [B, AB,..., A n−1B] is the formal reachability matrix for the pair (A, B). This abstract property is first characterized by a numerical rank criterion over the field of complex numbers. Then it is shown that reachability is generic if and only if k < m. It is hoped that the results presented will stimulate further research on polynomial output feedback controllers' for the delay-differential and multidiscrete-type systems.
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