Skip to main content
SpringerLink
Log in

Output feedback fault-tolerant control for a class of discrete-time fuzzy bilinear systems

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper studies the fault-tolerant control problem for a class of discrete-time fuzzy bilinear systems with unmeasurable states. A fuzzy detective observer is designed to detect the faults. Based on the fuzzy detective observer, a fuzzy controller is designed by solving a set of linear matrix inequalities (LMIs) to ensure that the closed-loop system without faults is asymptotically stable. For the discrete-time fuzzy bilinear system with faults, a fuzzy adaptive diagnostic observer is designed to estimate the faults by solving a set of LMIs. Then, a fuzzy faulttolerant controller is designed based on the fuzzy diagnostic observer to ensure that the closed-loop system with faults is asymptotically stable. At last, simulation results are presented to verify the effectiveness of the proposed output feedback fault-tolerant control method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. R. Mohler, and W. J. Kolodziej, “An overview of bilinear system theory and applications,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 10, no. 10, pp. 683–688, 2008. [click]

    MathSciNet  MATH  Google Scholar 

  2. H. Jerbi, “Global feedback stabilization of new class of bilinear systems,” Systems & Control Letters, vol. 42, no. 6, pp. 313–320, 2008. [click]

    MathSciNet  MATH  Google Scholar 

  3. S. Hanba and Y. Miyasato, “Output feedback stabilization of bilinear systems using dead-beat observers,” Automatica, vol. 37, no. 6, pp. 915–920, 2001. [click]

    Article  MathSciNet  MATH  Google Scholar 

  4. Z. D. Wang, H. Qiao, and K. J. Burnham, “On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters,” IEEE Transactions on Automatic Control, vol. 47, no. 4, pp. 640–646, 2002. [click]

    Article  MathSciNet  Google Scholar 

  5. J. S. Chiou, F. C. Kung, and T. H. S. Li, “Robust stabilization of a class of singularly perturbed discrete bilinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 6, pp. 1187–1191, 2000. [click]

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Bacic, M. Cannon, and B. Kouvaritakis, “Constrained control of SISO bilinear systems,” IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1443–1447, 2003. [click]

    Article  MathSciNet  Google Scholar 

  7. G. P. Lu, G. Feng, and Z. P. Jiang, “Saturated feedback stabilization of discrete-time descriptor bilinear systems,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1700–1704, 2007. [click]

    Article  MathSciNet  Google Scholar 

  8. Z. Mohamed, D. Mohamed, B. B. Latifa, and S. A. Harouna, “H ∞ filtering for singular bilinear systems with application to a single-link flexible-joint robot,” International Journal of Control, Automation and Systems, vol. 12, no. 3, pp. 590–598, 2014. [click]

    Article  Google Scholar 

  9. S. C. Tong and H. X. Li, “Fuzzy adaptive sliding-mode control for MIMO nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 3, pp. 354–360, 2003. [click]

    Article  Google Scholar 

  10. B. Chen, X. P. Liu, and S. C. Tong, “Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 287–300, 2007. [click]

    Article  Google Scholar 

  11. V. Vembarasan, P. Balasubramaniam, and C. S. Chan, “Robust synchronization of uncertain chaotic neural networks with randomly occurring uncertainties and non-fragile output coupling delayed feedback controllers,” Nonlinear Dynamics, vol. 78, no. 3, pp. 2031–2047, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. V. Vembarasan, P. Balasubramaniam, and C. S. Chan, “Non-fragile state observer design for neural networks with Markovian jumping parameters and time-delays,” Nonlinear Analysis: Hybrid Systems, vol. 14, no. 3, pp. 61–73, 2014. [click]

    MathSciNet  MATH  Google Scholar 

  13. Y. Y. Cao and P. M. Frank, “Stability analysis and synthesis of nonlinear time-delay system via linear Takagi-Sugino fuzzy models,” IEEE Transactions on Fuzzy Sets and Systems, vol. 24, no. 2, pp. 213–229, 2001. [click]

    Article  MathSciNet  MATH  Google Scholar 

  14. S. C. Tong, W. Wang, and L. J. Qu, “Decentralized robust control for uncertain T-S fuzzy large-scale systems with time-delay,” International Journal of Innovative Computing, Information and Control, vol. 3, no. 3, pp. 657–672, 2007.

    Google Scholar 

  15. H. J. Gao, and T. W. Chen, “Stabilization of nonlinear systems under variable sampling: A fuzzy control approach,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 5, pp. 972–983, 2007. [click]

    Article  MathSciNet  Google Scholar 

  16. T. H. S. Li, S. H. Tsai, and J. Z. Lee, “Robust H ∞ fuzzy control for a class of uncertain discrete fuzzy bilinear systems,” IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics, vol. 38, no. 2, pp. 510–527, 2008. [click]

    Article  MathSciNet  Google Scholar 

  17. T. H. S. Li, and S. H. Tsai, “T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 494–506, 2007. [click]

    Article  Google Scholar 

  18. T. T. Chen, S. H. Tsai, and C. L. Li, “Fuzzy control for T-S fuzzy bilinear systems with time-delay in state and control input,” Proc. of International Conference on System Science and Engineering, pp. 346–351, Macao, China, 2011. [click]

    Google Scholar 

  19. J. M. Li, and G. Zhang, “Robust H1 control for a class of multiple input fuzzy bilinear system with uncertainties,” Control Theory and Applications, vol. 26, no. 11, pp. 1298–1302, 2009.

    Google Scholar 

  20. J. M. Li, and G. Zhang, “Non-fragile guaranteed cost control of T-S fuzzy time-varying state and control delays systems with local bilinear models,” Iranian Journal of Fuzzy Systems, vol. 9, no. 2, pp. 1–19, 2012.

    MathSciNet  Google Scholar 

  21. J. X. Dong, and G. H. Yang, “Static output feedback control synthesis for discrete-time T-S fuzzy systems,” International Journal of Control, Automation and Systems, vol. 5, no. 3, pp. 349–354, 2007.

    Google Scholar 

  22. J. R. Li, and Z. L. Xia, “Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear systems,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 21, no. 3, pp. 1–19, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. J. R. Li, J. M. Li, and Z. L. Xia, “Delay-dependent generalized H 2 fuzzy static-output-feedback control for discrete T-S fuzzy bilinear stochastic systems with mixed delays,” Journal of Intelligent and Fuzzy Systems, vol. 25, no. 4, pp. 863–880, 2013. [click]

    MathSciNet  MATH  Google Scholar 

  24. D. Efimov, A. Zolghadri, and T. Raissi, “Actuator fault detection and compensation under feedback control,” Automatica, vol. 47, no. 8, pp. 1699–1705, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  25. W. Wang, and C. Y. Wen, “Adaptive actuator failure compensation for uncertain nonlinear systems with guaranteed transient performance,” Automatica, vol. 46, no. 12, pp. 2082–2091, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  26. M. Liu, X. B. Cao, P. Shi, “Fault estimation and tolerant control for T-S fuzzy stochastic systems,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 2, pp. 221–229, 2013. [click]

    Article  Google Scholar 

  27. M. Liu, X. B. Cao, P. Shi, “Fuzzy-model-based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 5, pp. 789–799, 2013. [click]

    Article  Google Scholar 

  28. W. Wang, and C. Y. Wen, “Adaptive compensation for infinite number of actuator failures or faults,” Automatica, vol. 47, no. 12, pp. 2197–2210, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  29. Y. Zhao, J. Lam, and H.J. Gao, “Fault detection for fuzzy systems with intermittent measurements,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 12, pp. 398–410, 2011. [click]

    Google Scholar 

  30. Q. K. Shen, B. Jiang, and V. Cocquempot, “Fault-tolerant control for T-S fuzzy systems with application to nearspace hypersonic vehicle with actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 4, pp. 652–665, 2012. [click]

    Article  Google Scholar 

  31. B. Jiang, Z. Gao, P. Shi, and Y. Xu, “Adaptive fault-tolerant tracking control of near-space vehicle using Takagi-Sugeno fuzzy models,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 1000–1007, 2010. [click]

    Article  Google Scholar 

  32. Q. K. Shen, B. Jiang, and C. Vincent, “Adaptive fuzzy observer-based Active fault-tolerant dynamic surface control for a class of nonlinear systems with actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 2, pp. 338–349, 2014. [click]

    Article  Google Scholar 

  33. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.

    Book  MATH  Google Scholar 

  34. D. S. Bernstein, Matrix Mathematics: Theory, Facts, and Formulas, Princeton University Press, 2009.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering, University of Ulsan, Daehak road 93, Namgu, Ulsan, 680-749, Korea

    Yang Yu & Kang-Hyun Jo

Authors
  1. Yang Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kang-Hyun Jo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kang-Hyun Jo.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Euntai Kim. This work was supported by 2015 Research Funds of University of Ulsan.

Yang Yu received the B.S. degree in Automation from Northeastern University, China, in 2002. He received the M.S. degree in Control Theory and Control Engineering from Liaoning University of Technology, China, in 2006. He is currently with Liaoning University of Technology as an Associate Professor. He is currently a Ph.D. candidate at the Graduate School of Electrical Engineering, University of Ulsan, Ulsan, Korea. His research interests include intelligent control and computer vision.

Kang-Hyun Jo received his Ph.D. degree from Osaka University, Japan, in 1997. He then joined the School of Electrical Eng., University of Ulsan right after having one year experience at ETRI as a post-doc research fellow. Dr. Jo has been active to serve for the societies for many years as directors of ICROS (Institute of Control, Robotics and Systems) and SICE (Society of Instrumentation and Control Engineers, Japan) as well as IEEE IES. He is currently contributing himself as an AE for a few journals, such as IJCAS (International Journal of Control, Automation and Systems), TCCI (Transactions on Computational Collective Intelligence) and IteN (IES Technical News, online publication of IEEE), TIE. He had involved in organizing many international conferences such as ICCAS, FCV, ICIC and IECON. He had visited for performing his research activity to Kyushu University, KIST and University of California Riverside. His research interest covers in a wide area where focuses on computer vision, robotics, and ambient intelligence.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, Y., Jo, KH. Output feedback fault-tolerant control for a class of discrete-time fuzzy bilinear systems. Int. J. Control Autom. Syst. 14, 486–494 (2016). https://doi.org/10.1007/s12555-014-0408-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-014-0408-6

Keywords

Search

Navigation