On the minimum order of a robust servocompensator

In recent papers [1]-[4], Davison et al. have given the characterization of a minimal-order robust error-driven servocompensator which achieves asymptotic tracking and disturbance rejection. In this note, we establish this minimality property by frequency domain methods. We show that any right coprime factorization of the controller, say
N_{r}(S)D_{r}(S)^{-1}
, must have all the elements of
D_{r}(s)
divisible by
\Phi(s)
, the minimal polynomial of the tracking and disturbance signal generator. Hence, its order must be at least
n_{0}.d(phi)
(n
0
=number of outputs,
d(\Phi)
= degree of
\Phi
).