Robust <I>H<sub>∞</sub> </I>Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators

Mohammad Karimi

doi:doi:10.11648/j.cse.20250901.11

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Robust H_∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators

Mohammad Karimi^*

Published in Control Science and Engineering (Volume 9, Issue 1)

Received: 11 April 2025 Accepted: 22 April 2025 Published: 29 May 2025

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Abstract

Time-delay in many systems and applications is often a source of instability and reduced system performance where among them Neutral time delay systems are a class of functional differential equations where the derivatives of the state not only depend on the current and past states but also explicitly on delay derivatives. These systems arise naturally in various engineering, biological and economic models where delays affect both the state and its rate of change. Also, the presence of uncertainties such as parameter variations, unmodeled dynamics and external disturbances further complicates the analysis and control of such systems. so, this paper deals with the robust H_∞ state-feedback control design for a class of uncertain systems subject to neutral Time-delay varying with multiple state and state derivatives delays is investigated in this paper. The parametric uncertainties are time varying and unknown but norm bounded. The main motivation of the paper is to develop a robust H_∞ controller, which ensures robust asymptotic stability of the system as well as a desired H_∞ performance and satisfy a prescribed γ performance level for all admissible uncertainties. By constructing a Lyapunov-Krasovskii functional, some sufficient conditions for the existence of the H_∞ state-feedback controller is derived in terms of linear matrix inequalities (LMI). Finally Numerical examples are provided to illustrate the effectiveness of the proposed method.

Published in	Control Science and Engineering (Volume 9, Issue 1)
DOI	10.11648/j.cse.20250901.11
Page(s)	1-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Robust H_∞, Control, Neutral Time-delay Systems, Lyapunov-Krasovskii Function, Stability Analysis, LMI

References

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[2]	Bhattacharyya, S. P. "Robust control under parametric uncertainty: An overview and recent results." Annual Reviews in Control 44 (2017): 45-77.
[3]	Barbosa, K. A.; Souza, C. E.; Trofino, A. Robust H₂ filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions. Syst. Control Lett. 2007, 54, 251–262.
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[5]	Zhang, R.; Hredzk, B. Distributed Finite-Time Multi-agent Control for DC Micro-grids With Time-delays. IEEE Trans. Smart Grid 2019, 10, 2692–2701.
[6]	Buzhin, I. G.; Mironov, Y. B. Evaluation of Telecommunication Equipment Delays in Software-Defined Networks. In Proceedings of the 2019 Systems of Signals Generating and Processing in the Field of on Board Communications, Moscow, Russia, 20–21 March 2019.
[7]	Lim, B.; Lee, J.; Jang, J.; Kim, K.; Park, Y. J.; Seo, K.; Shim, Y. Delayed Output Feedback Control for Gait Assistance With a Robotic Hip Exoskeleton. IEEE Trans. Robot. 2019, 35, 1055–1062.
[8]	Liu Y, Xing Z, Chen L, Xu J, Li Y, Wang H.
[9]	Control for a Class of Discrete-Time Systems via Data-Based Policy Iteration With Application to Wind Turbine Control. IEEE Access. 2019 Dec 26; 8: 14565-72.
[10]	Li, X.; Cao, J.; Ho, D. W. C. Impulsive Control of Nonlinear Systems With Time-Varying Delay and Applications. IEEE Trans. Cyber. 2020, 50, 2661–2673.
[11]	Sun, Z. Y.; Song, Z. B.; Li, T.; Yang, S. H. Output feedback stabilization for high-order uncertain feedforward time-delay nonlinear systems. J. Frankl. Inst.-Eng. Appl. Math. 2015, 352, 5308–5326.
[12]	Liu, Hao. Robust control for quadrotors with multiple time-varying uncertainties and delays. IEEE Transactions on Industrial Electronics, 2017, 64.2: 1303-1312.‏
[13]	Karimi, Mohammad. "Further results on robust H_∞ control design for uncertain time-delay systems with actuator delay: application to PMSG machine." Systems Science & Control Engineering 6.1, 2018: 510-517.
[14]	Mobayen, Saleh, and Dumitru Baleanu. (). Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control. Journal of Vibration and Control 23.8: 2017, 1285-1295.
[15]	Chen, Yonggang, Shumin Fei, and Yongmin Li. "Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback." Automatica 52, 2015, 242-247.
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[17]	Meng, Xin, et al. "Robust control for a class of uncertain neutral-type systems with time-varying delays." Asian Journal of Control 23.3, 2021, 1454-1465.
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APA Style

Karimi, M. (2025). Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators. Control Science and Engineering, 9(1), 1-9. https://doi.org/10.11648/j.cse.20250901.11

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ACS Style

Karimi, M. Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators. Control Sci. Eng. 2025, 9(1), 1-9. doi: 10.11648/j.cse.20250901.11

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AMA Style

Karimi M. Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators. Control Sci Eng. 2025;9(1):1-9. doi: 10.11648/j.cse.20250901.11

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@article{10.11648/j.cse.20250901.11,
  author = {Mohammad Karimi},
  title = {Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators
},
  journal = {Control Science and Engineering},
  volume = {9},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.cse.20250901.11},
  url = {https://doi.org/10.11648/j.cse.20250901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cse.20250901.11},
  abstract = {Time-delay in many systems and applications is often a source of instability and reduced system performance where among them Neutral time delay systems are a class of functional differential equations where the derivatives of the state not only depend on the current and past states but also explicitly on delay derivatives. These systems arise naturally in various engineering, biological and economic models where delays affect both the state and its rate of change. Also, the presence of uncertainties such as parameter variations, unmodeled dynamics and external disturbances further complicates the analysis and control of such systems. so, this paper deals with the robust H_∞ state-feedback control design for a class of uncertain systems subject to neutral Time-delay varying with multiple state and state derivatives delays is investigated in this paper. The parametric uncertainties are time varying and unknown but norm bounded. The main motivation of the paper is to develop a robust H∞ controller, which ensures robust asymptotic stability of the system as well as a desired H∞ performance and satisfy a prescribed γ performance level for all admissible uncertainties. By constructing a Lyapunov-Krasovskii functional, some sufficient conditions for the existence of the H∞ state-feedback controller is derived in terms of linear matrix inequalities (LMI). Finally Numerical examples are provided to illustrate the effectiveness of the proposed method.
},
 year = {2025}
}

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TY  - JOUR
T1  - Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators

AU  - Mohammad Karimi
Y1  - 2025/05/29
PY  - 2025
N1  - https://doi.org/10.11648/j.cse.20250901.11
DO  - 10.11648/j.cse.20250901.11
T2  - Control Science and Engineering
JF  - Control Science and Engineering
JO  - Control Science and Engineering
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2994-7421
UR  - https://doi.org/10.11648/j.cse.20250901.11
AB  - Time-delay in many systems and applications is often a source of instability and reduced system performance where among them Neutral time delay systems are a class of functional differential equations where the derivatives of the state not only depend on the current and past states but also explicitly on delay derivatives. These systems arise naturally in various engineering, biological and economic models where delays affect both the state and its rate of change. Also, the presence of uncertainties such as parameter variations, unmodeled dynamics and external disturbances further complicates the analysis and control of such systems. so, this paper deals with the robust H_∞ state-feedback control design for a class of uncertain systems subject to neutral Time-delay varying with multiple state and state derivatives delays is investigated in this paper. The parametric uncertainties are time varying and unknown but norm bounded. The main motivation of the paper is to develop a robust H∞ controller, which ensures robust asymptotic stability of the system as well as a desired H∞ performance and satisfy a prescribed γ performance level for all admissible uncertainties. By constructing a Lyapunov-Krasovskii functional, some sufficient conditions for the existence of the H∞ state-feedback controller is derived in terms of linear matrix inequalities (LMI). Finally Numerical examples are provided to illustrate the effectiveness of the proposed method.

VL  - 9
IS  - 1
ER  -

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Author Information

Mohammad Karimi

Department of Electrical Engineering, Tafresh University, Tafresh, Iran

Contact Email

http://orcid.org/0009-0003-3885-6728

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Plain Text BibTeX RIS

APA Style

Karimi, M. (2025). Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators. Control Science and Engineering, 9(1), 1-9. https://doi.org/10.11648/j.cse.20250901.11

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ACS Style

Karimi, M. Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators. Control Sci. Eng. 2025, 9(1), 1-9. doi: 10.11648/j.cse.20250901.11

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AMA Style

Karimi M. Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators. Control Sci Eng. 2025;9(1):1-9. doi: 10.11648/j.cse.20250901.11

Copy | Download

@article{10.11648/j.cse.20250901.11,
  author = {Mohammad Karimi},
  title = {Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators
},
  journal = {Control Science and Engineering},
  volume = {9},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.cse.20250901.11},
  url = {https://doi.org/10.11648/j.cse.20250901.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cse.20250901.11},
  abstract = {Time-delay in many systems and applications is often a source of instability and reduced system performance where among them Neutral time delay systems are a class of functional differential equations where the derivatives of the state not only depend on the current and past states but also explicitly on delay derivatives. These systems arise naturally in various engineering, biological and economic models where delays affect both the state and its rate of change. Also, the presence of uncertainties such as parameter variations, unmodeled dynamics and external disturbances further complicates the analysis and control of such systems. so, this paper deals with the robust H_∞ state-feedback control design for a class of uncertain systems subject to neutral Time-delay varying with multiple state and state derivatives delays is investigated in this paper. The parametric uncertainties are time varying and unknown but norm bounded. The main motivation of the paper is to develop a robust H∞ controller, which ensures robust asymptotic stability of the system as well as a desired H∞ performance and satisfy a prescribed γ performance level for all admissible uncertainties. By constructing a Lyapunov-Krasovskii functional, some sufficient conditions for the existence of the H∞ state-feedback controller is derived in terms of linear matrix inequalities (LMI). Finally Numerical examples are provided to illustrate the effectiveness of the proposed method.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Robust H∞ Control Approach for Neutral Time-delay Systems Under Uncertainty Consideration: A Case Study on Permanent Magnet Synchronous Generators

AU  - Mohammad Karimi
Y1  - 2025/05/29
PY  - 2025
N1  - https://doi.org/10.11648/j.cse.20250901.11
DO  - 10.11648/j.cse.20250901.11
T2  - Control Science and Engineering
JF  - Control Science and Engineering
JO  - Control Science and Engineering
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2994-7421
UR  - https://doi.org/10.11648/j.cse.20250901.11
AB  - Time-delay in many systems and applications is often a source of instability and reduced system performance where among them Neutral time delay systems are a class of functional differential equations where the derivatives of the state not only depend on the current and past states but also explicitly on delay derivatives. These systems arise naturally in various engineering, biological and economic models where delays affect both the state and its rate of change. Also, the presence of uncertainties such as parameter variations, unmodeled dynamics and external disturbances further complicates the analysis and control of such systems. so, this paper deals with the robust H_∞ state-feedback control design for a class of uncertain systems subject to neutral Time-delay varying with multiple state and state derivatives delays is investigated in this paper. The parametric uncertainties are time varying and unknown but norm bounded. The main motivation of the paper is to develop a robust H∞ controller, which ensures robust asymptotic stability of the system as well as a desired H∞ performance and satisfy a prescribed γ performance level for all admissible uncertainties. By constructing a Lyapunov-Krasovskii functional, some sufficient conditions for the existence of the H∞ state-feedback controller is derived in terms of linear matrix inequalities (LMI). Finally Numerical examples are provided to illustrate the effectiveness of the proposed method.

VL  - 9
IS  - 1
ER  -

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