Static output feedback canonical forms

Abstract

Abstract We construct complete static output feedback (SOF) invariants and canonical forms of the set of strictly proper full rank, rational, transfer function matrices. We consider the induced action of the SOF group on the set of Plücker coordinates. Some of them are SOF-invariant and that some others vary linearly with the entries of the feedback gain. Further SOF-invariants are constructed based on the consistency conditions of linear systems of equations. The pair of the above two lists of invariants is complete. The proof is given, introducing a new type of factorization. We construct a SOF-canonical form. We apply the results to the class of systems with two inputs two outputs, characterizing the SOF-equivalence classes in the case of four states as to the property of SOF-pole assignability and calculating the constrained dynamics in the case of more than four states.