A theorem on the effects of compensator poles on feedback system zeros

At the system matrix level, the well-known proposition that the poles of a feedback compensator become the zeros of the closed-loop system, is examined via a module-theoretic framework. In particular, the main theorem creates an epimorphism from the zero module of the closed-loop system onto the pole module of the compensator, thereby establishing that the zero module of the closed-loop system does indeed contain the pole module of the compensator in a factor module sense. The proof, presented in detail, requires no restrictive minimality or squareness conditions. Implications and interpretations are also examined