Active vibration control for fractional order systems based on multiple region eigenvalue assignment

Binxin He; Hao Liu; Binxin He; Hao Liu

doi:10.3934/era.2025211

Electronic Research Archive

2025, Volume 33, Issue 8: 4693-4722. doi: 10.3934/era.2025211

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Research article

Active vibration control for fractional order systems based on multiple region eigenvalue assignment

Binxin He ¹,
Hao Liu ^{1,2
,
,}

1.
School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2.
Shenzhen Research Institute, Nanjing University of Aeronautics and Astronautics, Shenzhen 518110, China

Received: 13 June 2025 Revised: 20 July 2025 Accepted: 25 July 2025 Published: 14 August 2025

This work addresses active vibration control for fractional-order systems based on a multiple region eigenvalue assignment. First, we propose the selection criteria of fractional-order multiple stability regions and define multiple stability regions by generalized linear matrix inequality. Based on the inverse eigenvalue problem theory, we give the sufficient condition for solving the feedback control matrix under multiple region eigenvalue assignment and present the expression of the feedback control matrix. Then, we propose a numerical algorithm for solving this problem, which improves the control performance. Finally, we verify the feasibility and effectiveness of the proposed method through numerical examples of fractional-order simulation and actual physical systems.
- fractional derivative model,
- active vibration control,
- region eigenvalue assignment,
- linear matrix inequality,
- inverse eigenvalue problem
Citation: Binxin He, Hao Liu. Active vibration control for fractional order systems based on multiple region eigenvalue assignment[J]. Electronic Research Archive, 2025, 33(8): 4693-4722. doi: 10.3934/era.2025211

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Abstract

This work addresses active vibration control for fractional-order systems based on a multiple region eigenvalue assignment. First, we propose the selection criteria of fractional-order multiple stability regions and define multiple stability regions by generalized linear matrix inequality. Based on the inverse eigenvalue problem theory, we give the sufficient condition for solving the feedback control matrix under multiple region eigenvalue assignment and present the expression of the feedback control matrix. Then, we propose a numerical algorithm for solving this problem, which improves the control performance. Finally, we verify the feasibility and effectiveness of the proposed method through numerical examples of fractional-order simulation and actual physical systems.

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