We present a constructive solution to the problem of full output feedback equivalence, of linear, minimal, time-invariant systems.\r\nThe equivalence relation on the set of systems is transformed to another on the set of invertible block Bezout/Hankel matrices\r\nusing the isotropy subgroups of the full state feedback group and the full output injection group. The transformation achieving\r\nequivalence is calculated solving linear systems of equations.We give a polynomial version of the results proving that two systems\r\nare full output feedback equivalent, if and only if they have the same family of generalized Bezoutians. We present a new set of\r\noutput feedback invariant polynomials that generalize the breakaway polynomial of scalar systems.
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