Invariants and canonical forms for output feedback

In this paper we announce some new results on the problem of classifying linear systems up to equivalence under change of bases in the input and output spaces and transformations by output feedback. In classical, root-locus terminology, we now know that a scalar system is completely characterized, modulo feedback, by the locations of its zeroes and its real and complex "break-away" points. In the multivariable case, a classification by such a complete set of invariants is out of the question, but we do give positive results for a generic class of systems - the class of nondegenerate systems which were introduced in the study of root-loci and output feedback pole-assignment in the late 1970\´s and early 1980\´s.