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

doi:10.1007/s11424-022-1361-8

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (6): 2046-2061.DOI: 10.1007/s11424-022-1361-8

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

DUAN Guang-Ren^1,2, ZHOU Bin²

1. The Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen 518055, China;
2. The Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China

Received:2021-09-22 Revised:2021-10-25 Online:2022-11-25 Published:2022-12-23
Supported by:
This work was supported by the Science Center Program of the National Natural Science Foundation of China under Grant No. 62188101, the Major Program of National Natural Science Foundation of China under Grant Nos. 61690210 and 61690212, the National Natural Science Foundation of China under Grant No. 61333003, and the Self-Planned Task of State Key Laboratory of Robotics and System (HIT) under Grant No. SKLRS201716A.

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DUAN Guang-Ren, ZHOU Bin. Fully Actuated System Approach for Linear Systems Control: A Frequency-Domain Solution[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2046-2061.

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 full-actuation 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.

Key words: Column reduced, factorization, first-order linear state-space systems, high-order fully actuated systems, polynomial matrix description, right coprime

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