On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems

Bin Zhou; Jiacheng Dong; Guang Ren Duan

doi:10.1109/CFASTA57821.2023.10243307

On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems

Bin Zhou
, Jiacheng Dong
, Guang Ren Duan

School of Astronautics

Harbin Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

For a linear time-invariant (LTI) system, controllability is equivalent to that it can be transformed into a high-order fully actuated system (HOFA). In this note, it is demonstrated that this is not the case for linear time-varying (LTV) systems even in the single input case. This paper points out that an LTV system can be transformed into a standard HOFA system if and only if its controllability matrix defined in the Silverman criterion is nonsingular for any time, which is only sufficient but not necessary for the controllability of the system. In addition, if the controllability matrix defined in the Silverman criterion is not nonsingular for any time, a degenerated HOFA system might be obtained. Some simple examples are given to demonstrate the reported facts.

Original language	English
Title of host publication	Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	49-53
Number of pages	5
ISBN (Electronic)	9798350332162
DOIs	https://doi.org/10.1109/CFASTA57821.2023.10243307
State	Published - 2023
Event	2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 - Qingdao, China Duration: 14 Jul 2023 → 16 Jul 2023

Publication series

Name	Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023

Conference

Conference	2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023
Country/Territory	China
City	Qingdao
Period	14/07/23 → 16/07/23

Keywords

Linear time-varying systems
high-order fully actuated systems
state transformation

Access to Document

10.1109/CFASTA57821.2023.10243307

Cite this

Zhou, B., Dong, J., & Duan, G. R. (2023). On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems. In Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 (pp. 49-53). (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CFASTA57821.2023.10243307

Zhou, Bin ; Dong, Jiacheng ; Duan, Guang Ren. / On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems. Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. pp. 49-53 (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023).

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title = "On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems",

abstract = "For a linear time-invariant (LTI) system, controllability is equivalent to that it can be transformed into a high-order fully actuated system (HOFA). In this note, it is demonstrated that this is not the case for linear time-varying (LTV) systems even in the single input case. This paper points out that an LTV system can be transformed into a standard HOFA system if and only if its controllability matrix defined in the Silverman criterion is nonsingular for any time, which is only sufficient but not necessary for the controllability of the system. In addition, if the controllability matrix defined in the Silverman criterion is not nonsingular for any time, a degenerated HOFA system might be obtained. Some simple examples are given to demonstrate the reported facts.",

keywords = "Linear time-varying systems, high-order fully actuated systems, state transformation",

author = "Bin Zhou and Jiacheng Dong and Duan, \{Guang Ren\}",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023 ; Conference date: 14-07-2023 Through 16-07-2023",

year = "2023",

doi = "10.1109/CFASTA57821.2023.10243307",

language = "英语",

series = "Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023",

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Zhou, B, Dong, J & Duan, GR 2023, On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems. in Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023, Institute of Electrical and Electronics Engineers Inc., pp. 49-53, 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023, Qingdao, China, 14/07/23. https://doi.org/10.1109/CFASTA57821.2023.10243307

On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems. / Zhou, Bin; Dong, Jiacheng; Duan, Guang Ren.
Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 49-53 (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Dong, Jiacheng

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N2 - For a linear time-invariant (LTI) system, controllability is equivalent to that it can be transformed into a high-order fully actuated system (HOFA). In this note, it is demonstrated that this is not the case for linear time-varying (LTV) systems even in the single input case. This paper points out that an LTV system can be transformed into a standard HOFA system if and only if its controllability matrix defined in the Silverman criterion is nonsingular for any time, which is only sufficient but not necessary for the controllability of the system. In addition, if the controllability matrix defined in the Silverman criterion is not nonsingular for any time, a degenerated HOFA system might be obtained. Some simple examples are given to demonstrate the reported facts.

AB - For a linear time-invariant (LTI) system, controllability is equivalent to that it can be transformed into a high-order fully actuated system (HOFA). In this note, it is demonstrated that this is not the case for linear time-varying (LTV) systems even in the single input case. This paper points out that an LTV system can be transformed into a standard HOFA system if and only if its controllability matrix defined in the Silverman criterion is nonsingular for any time, which is only sufficient but not necessary for the controllability of the system. In addition, if the controllability matrix defined in the Silverman criterion is not nonsingular for any time, a degenerated HOFA system might be obtained. Some simple examples are given to demonstrate the reported facts.

KW - Linear time-varying systems

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Zhou B, Dong J, Duan GR. On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems. In Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023. Institute of Electrical and Electronics Engineers Inc. 2023. p. 49-53. (Proceedings of the 2nd Conference on Fully Actuated System Theory and Applications, CFASTA 2023). doi: 10.1109/CFASTA57821.2023.10243307

On Transforming Single Input Linear Time-Varying Systems into High-order Fully Actuated Systems

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