Fully Actuated System Approach for Linear Systems Control:A Frequency-Domain Solution

This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system model.This method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD model.Both continuous-time and discrete-time linear systems are considered.Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.