Fully actuated system approach for high-order linear systems with high-order input derivatives (Q6601006)

This paper develops a frequency-domain approach for converting a high-order linear system with high-order input derivatives into an FAS model using three distinct methods. The key contributions of this work are as follows: 1. For a controllable high-order linear system, the authors employ the polynomial matrix description (PMD) -- a frequency-domain representation of a linear system -- and establish that an FAS model can be obtained if the factorization polynomial matrix is column-reduced. 2. To address the issue of non-square matrices encountered in the direct approach, they transform the original system into its observability canonical form via linearization, allowing to derive an explicit expression for the transformed state. 3. Additionally, a novel transformation is introduced to overcome the limitation imposed by the system's order on the order of input derivatives in the linearization method, providing an alternative FAS model. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed methods.