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Robust Decentralized Dissipative Control Design for Uncertain Fractional-Order Interconnected Systems via Non-Fragile State Feedback
1
Department of Basic Sciences, TNU--University of Economics and Business Administration, Thai Nguyen 250000, Vietnam
2
Department of Mathematics and Informatics, TNU--University of Sciences, Thai Nguyen 250000, Vietnam
3
Faculty of Fundamental and Applied Sciences, TNU--University of Technology, Thai Nguyen 250000, Vietnam
Corresponding Author:
Nguyen Thi Phuong,
[email protected]
Volume 2, Issue 1
2026
Received: 16 January 2026
Accepted: 11 March 2026
Published: 15 March 2026
Article Information
Published in
Journal of Nonlinear Dynamics and Applications
Volume/Issue
Volume 2, Issue 1, 2026
Pages
47-60
Abstract
This study examines the problem of decentralized non-fragile dissipative control for a category of fractional-order linear uncertain large-scale systems. We assume that the subsystems uncertainty is norm-bounded and time-varying. Furthermore, we assume that the state-feedback gains for subsystems of the fractional-order large-scale system have norm-bounded controller gain variations. To achieve our goal, we introduce the concept of $(S, Q, R)-$dissipativity for fractional-order interconnected systems. By using this definition and mathematical transformations with fractional calculus, a decentralized non-fragile state-feedback controller is designed so that the closed-loop interconnected systems become asymptotically stable and satisfy a dissipative performance index. By utilizing the fractional-order Lyapunov method, sufficient LMI-based conditions are obtained to guarantee the existence of the desired controllers. Additionally, we provide a parameterized characterization of the robust non-fragile dissipative controller in terms of feasible solutions to certain LMIs. Finally, a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed control design approach.
Graphical Abstract
Keywords
decentralized non-fragile dissipative control
Fractional-order interconnected systems
fractional-order lyapunov method
linear matrix inequalities
Data Availability Statement
Data will be made available on request.
Funding
This work was supported by the Thai Nguyen University -- University of Technology in Vietnam.
Conflicts of Interest
The authors declare no conflicts of interest.
AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable.
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APA Style
Binh, T. N., Thuan, M. V., & Phuong, N. T. (2026). Robust Decentralized Dissipative Control Design for Uncertain Fractional-Order Interconnected Systems via Non-Fragile State Feedback. Journal of Nonlinear Dynamics and Applications, 2(1), 47–60. https://doi.org/10.62762/JNDA.2026.759291
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TY - JOUR AU - Binh, Tran Nguyen AU - Thuan, Mai Viet AU - Phuong, Nguyen Thi PY - 2026 DA - 2026/03/15 TI - Robust Decentralized Dissipative Control Design for Uncertain Fractional-Order Interconnected Systems via Non-Fragile State Feedback JO - Journal of Nonlinear Dynamics and Applications T2 - Journal of Nonlinear Dynamics and Applications JF - Journal of Nonlinear Dynamics and Applications VL - 2 IS - 1 SP - 47 EP - 60 DO - 10.62762/JNDA.2026.759291 UR - https://www.icck.org/article/abs/JNDA.2026.759291 KW - decentralized non-fragile dissipative control KW - Fractional-order interconnected systems KW - fractional-order lyapunov method KW - linear matrix inequalities AB - This study examines the problem of decentralized non-fragile dissipative control for a category of fractional-order linear uncertain large-scale systems. We assume that the subsystems uncertainty is norm-bounded and time-varying. Furthermore, we assume that the state-feedback gains for subsystems of the fractional-order large-scale system have norm-bounded controller gain variations. To achieve our goal, we introduce the concept of $(S, Q, R)-$dissipativity for fractional-order interconnected systems. By using this definition and mathematical transformations with fractional calculus, a decentralized non-fragile state-feedback controller is designed so that the closed-loop interconnected systems become asymptotically stable and satisfy a dissipative performance index. By utilizing the fractional-order Lyapunov method, sufficient LMI-based conditions are obtained to guarantee the existence of the desired controllers. Additionally, we provide a parameterized characterization of the robust non-fragile dissipative controller in terms of feasible solutions to certain LMIs. Finally, a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed control design approach. SN - 3069-6313 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Binh2026Robust,
author = {Tran Nguyen Binh and Mai Viet Thuan and Nguyen Thi Phuong},
title = {Robust Decentralized Dissipative Control Design for Uncertain Fractional-Order Interconnected Systems via Non-Fragile State Feedback},
journal = {Journal of Nonlinear Dynamics and Applications},
year = {2026},
volume = {2},
number = {1},
pages = {47-60},
doi = {10.62762/JNDA.2026.759291},
url = {https://www.icck.org/article/abs/JNDA.2026.759291},
abstract = {This study examines the problem of decentralized non-fragile dissipative control for a category of fractional-order linear uncertain large-scale systems. We assume that the subsystems uncertainty is norm-bounded and time-varying. Furthermore, we assume that the state-feedback gains for subsystems of the fractional-order large-scale system have norm-bounded controller gain variations. To achieve our goal, we introduce the concept of \$(S, Q, R)-\$dissipativity for fractional-order interconnected systems. By using this definition and mathematical transformations with fractional calculus, a decentralized non-fragile state-feedback controller is designed so that the closed-loop interconnected systems become asymptotically stable and satisfy a dissipative performance index. By utilizing the fractional-order Lyapunov method, sufficient LMI-based conditions are obtained to guarantee the existence of the desired controllers. Additionally, we provide a parameterized characterization of the robust non-fragile dissipative controller in terms of feasible solutions to certain LMIs. Finally, a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed control design approach.},
keywords = {decentralized non-fragile dissipative control, Fractional-order interconnected systems, fractional-order lyapunov method, linear matrix inequalities},
issn = {3069-6313},
publisher = {Institute of Central Computation and Knowledge}
}
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