Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System

Lingyan Hu

doi:doi:10.11648/j.ijssam.20160102.11

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Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System

Lingyan Hu

Published in International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 2)

Received: 23 May 2016 Accepted: 3 June 2016 Published: 23 June 2016

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Abstract

Non-fragile fault-tolerant controller is designed for a class of linear uncertain time-delayed systems. Two cases of controller perturbation are investigated in view of different application conditions. One case is the controller gain attenuation, the other is random uncertainty caused by noise possibly existing in an industrial field. The controller to be designed can guarantee systems to have robust fault-tolerant capability and non-fragility. Sufficient conditions for the existence of such controllers are derived basing on Lyapunov stability theory and LMI method. A numerical example of a beam reheating furnace is given. And computation results demonstrate the effectiveness of the proposed algorithm.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 2)
DOI	10.11648/j.ijssam.20160102.11
Page(s)	8-15
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), 2024. Published by Science Publishing Group

Keywords

Fault-Tolerant Control, Non-fragility, Uncertain Time-Delayed System, Linear Matrix Inequality (LMI)

References

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[2]	D. Rotondoa, F. Nejjaria, and V. Puig, “A virtual actuator and sensor approach for fault tolerant control of LPV systems,” Journal of Process Control, vol. 24, pp. 203-222, March 2014.
[3]	J. Jin and Y. Xiang, “Fault-tolerant control systems: a comparative study between active and passive approaches,” Annual Reviews in Control, vol. 36, pp. 60-72, April 2012.
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[6]	L. Y. Hu, “Robust fault-tolerant control of uncertain systems with state and control timed-delays,” the Ninth International Conference on Natural Computation, China, pp. 1665-1669, July 2013.
[7]	L. Y. Hu, “Design of Fault-tolerant Controllers with Non-fragile and Memory characteristics for a Class of Uncertain Time-delayed Systems”, unpublished.
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[12]	H. B. Sun, S. H. Li, and C. Y. Sun, “Non-fragile adaptive fault-tolerant controller design for an airbreathing hypersonic vehicle,” Proceedings of the 31st Chinese Control, China, pp. 453-458, July 2012.
[13]	C. H. Liena, http://www.sciencedirect.com/science/article/pii/S0960077905012014 - cor1mailto:chlien@isu.edu.twW. C. Chenga, C. H. Tsaia, and K. W. Yub, “Non-fragile observer-based controls of linear system via LMI approach,” Chaos, Solitons & Fractals, Vol. 32, pp. 1530-1537, May 2007.
[14]	J. S. Yee, G. H. Yang, and J. L. Wang, “Non-fragile guaranteed cost control for discrete-time uncertain linear systems,” International Journal of Systems Science, Vol. 32, pp. 845-853, July 2001.
[15]	J. H. Parka, “Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections,” International Journal of Systems Science, Vol. 35, pp. 233-241, April 2004.
[16]	M. Wu, Y. He, and J. H. She, Stability Analysis and Robust Control of Time-delay Systems. Beijing: Science press, 2009.

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Lingyan Hu. (2016). Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System. International Journal of Systems Science and Applied Mathematics, 1(2), 8-15. https://doi.org/10.11648/j.ijssam.20160102.11

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ACS Style

Lingyan Hu. Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System. Int. J. Syst. Sci. Appl. Math. 2016, 1(2), 8-15. doi: 10.11648/j.ijssam.20160102.11

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AMA Style

Lingyan Hu. Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System. Int J Syst Sci Appl Math. 2016;1(2):8-15. doi: 10.11648/j.ijssam.20160102.11

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@article{10.11648/j.ijssam.20160102.11,
  author = {Lingyan Hu},
  title = {Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {2},
  pages = {8-15},
  doi = {10.11648/j.ijssam.20160102.11},
  url = {https://doi.org/10.11648/j.ijssam.20160102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160102.11},
  abstract = {Non-fragile fault-tolerant controller is designed for a class of linear uncertain time-delayed systems. Two cases of controller perturbation are investigated in view of different application conditions. One case is the controller gain attenuation, the other is random uncertainty caused by noise possibly existing in an industrial field. The controller to be designed can guarantee systems to have robust fault-tolerant capability and non-fragility. Sufficient conditions for the existence of such controllers are derived basing on Lyapunov stability theory and LMI method. A numerical example of a beam reheating furnace is given. And computation results demonstrate the effectiveness of the proposed algorithm.},
 year = {2016}
}

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TY  - JOUR
T1  - Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System
AU  - Lingyan Hu
Y1  - 2016/06/23
PY  - 2016
N1  - https://doi.org/10.11648/j.ijssam.20160102.11
DO  - 10.11648/j.ijssam.20160102.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 8
EP  - 15
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20160102.11
AB  - Non-fragile fault-tolerant controller is designed for a class of linear uncertain time-delayed systems. Two cases of controller perturbation are investigated in view of different application conditions. One case is the controller gain attenuation, the other is random uncertainty caused by noise possibly existing in an industrial field. The controller to be designed can guarantee systems to have robust fault-tolerant capability and non-fragility. Sufficient conditions for the existence of such controllers are derived basing on Lyapunov stability theory and LMI method. A numerical example of a beam reheating furnace is given. And computation results demonstrate the effectiveness of the proposed algorithm.
VL  - 1
IS  - 2
ER  -

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Author Information

Lingyan Hu

College of Information Engineering, Dalian University, Dalian, China

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APA Style

Lingyan Hu. (2016). Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System. International Journal of Systems Science and Applied Mathematics, 1(2), 8-15. https://doi.org/10.11648/j.ijssam.20160102.11

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ACS Style

Lingyan Hu. Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System. Int. J. Syst. Sci. Appl. Math. 2016, 1(2), 8-15. doi: 10.11648/j.ijssam.20160102.11

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AMA Style

Lingyan Hu. Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System. Int J Syst Sci Appl Math. 2016;1(2):8-15. doi: 10.11648/j.ijssam.20160102.11

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@article{10.11648/j.ijssam.20160102.11,
  author = {Lingyan Hu},
  title = {Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {2},
  pages = {8-15},
  doi = {10.11648/j.ijssam.20160102.11},
  url = {https://doi.org/10.11648/j.ijssam.20160102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160102.11},
  abstract = {Non-fragile fault-tolerant controller is designed for a class of linear uncertain time-delayed systems. Two cases of controller perturbation are investigated in view of different application conditions. One case is the controller gain attenuation, the other is random uncertainty caused by noise possibly existing in an industrial field. The controller to be designed can guarantee systems to have robust fault-tolerant capability and non-fragility. Sufficient conditions for the existence of such controllers are derived basing on Lyapunov stability theory and LMI method. A numerical example of a beam reheating furnace is given. And computation results demonstrate the effectiveness of the proposed algorithm.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Non-fragile Fault-Tolerant Control with Gain Perturbation for a Linear Uncertain Time-Delayed System
AU  - Lingyan Hu
Y1  - 2016/06/23
PY  - 2016
N1  - https://doi.org/10.11648/j.ijssam.20160102.11
DO  - 10.11648/j.ijssam.20160102.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 8
EP  - 15
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20160102.11
AB  - Non-fragile fault-tolerant controller is designed for a class of linear uncertain time-delayed systems. Two cases of controller perturbation are investigated in view of different application conditions. One case is the controller gain attenuation, the other is random uncertainty caused by noise possibly existing in an industrial field. The controller to be designed can guarantee systems to have robust fault-tolerant capability and non-fragility. Sufficient conditions for the existence of such controllers are derived basing on Lyapunov stability theory and LMI method. A numerical example of a beam reheating furnace is given. And computation results demonstrate the effectiveness of the proposed algorithm.
VL  - 1
IS  - 2
ER  -

Copy | Download