Feedback invariants of supplementary pairs of matrices (Q1388104)

Given a linear system defined by a pair of matrices \((A,B)\), to any controlled invariant subspace \(S\) one can associate the restriction of \((A,B)\) to \(S\) and the corresponding quotient. A complete set of invariants for the pair \((A,B)\) under feedback equivalence is known to consists of the controllability indices and the invariant factors of the pair. The paper is devoted to the problem of characterizing a complete set of invariants for the feedback equivalence relation of the matrix pair \((A,B)\) when its restriction and quotient with respect to a given invariant subspace is prescribed and the restriction is assumed to be controllable.