Calculation of the minimal dimension kth-order robust servoregulator

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 in Huang (1992) when the given exosystem is semisimple. This paper further provides 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.