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 , must have all the elements of divisible by , the minimal polynomial of the tracking and disturbance signal generator. Hence, its order must be at least (n0=number of outputs, = degree of ).