Fully actuated system approach for high-order linear systems with high-order input derivatives

This paper presents a frequency-domain method for transforming a class of high-order linear systems with high-order derivatives of input into the corresponding full-actuated system (FAS) models. Based on the coprime factorisation theory, it is proved that under the condition that the factorisation polynomial matrix is column reduced, a direct method can be given to transform the original system into an FAS model. Regard the non-square problem faced by the direct method, two different methods are given to present the explicit expression of the transformed state. The first one is given for the case the order of system is higher than that of input, in which the system is transformed into the corresponding observability canonical form. The other one considers the opposite case, in which the model reduction method is adopted. Three numerical examples are given to illustrate the proposed theories.