The design of a minimal dimension kth-order robust servoregulator requires calculation of the minimal polynomial of a class of matrices defined by the given exosystem, A characterization of the minimal polynomial of this class of matrices was given recently in [8] when the given exosystem is semisimple. This paper will further provide a characterization of this class of matrices in the general case, This result leads to a straightforward and efficient procedure to calculate the minimal dimension kth-order robust servoregulator.