Complete feedback invariant form for linear output feedback

It will be shown that a complete set of feedback invariants for linear (or static) output feedback is explicitly defined under the Grassman space framework. Specifically, it is established that the Grassmann invariant form of linear multivariable system (rigorously, multivector nonzero decomposable form over a rational vector space associated with transfer function matrix), presents a global, minimal and complete feedback invariant form in linear output feedback pole-assignment condition. A former negative preclusion, nonclosed orbit problem for output feedback equivalence in linear algebraic group approach, is re-analyzed in the Grassmann invariant condition (so called, Plucker matrix full-rank condition). A constructive algorithm for the complete feedback invariant form is given and illustrated in a concrete way.