Solvability of the decoupling problem for linear constant (A,B,C,D)-quadruples with regular output feedback

The aim of this paper is to deal with the general decoupling problem of linear constant (
A, B, C, D
)-quadruples under the assumption of (regular) output feedback. In its most general setting, this problem was hitherto unsolved. Here we give a complete characterization of solutions by (regular) output feedback by means of necessary and sufficient conditions of existence. They generalize the result previously obtained by Denham [4] for the linear constant (
A, B, C
)-triples.