Skip to main content
Springer Nature Link
Log in

Delay-dependent non-fragile H ∞ filtering for uncertain fuzzy systems based on switching fuzzy model and piecewise Lyapunov function

  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

This paper is concerned with the non-fragile H ∞ filter design problem for uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay. To begin with, the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Then, based on the piecewise Lyapunov function and matrix decoupling technique, a new delay-dependent non-fragile H ∞ filtering method is proposed for the switching fuzzy system. The proposed condition is less conservative than the previous results. Since only a set of LMIs is involved, the filter parameters can be solved directly. Finally, a design example is provided to illustrate the validity of the proposed method.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. T. Takagi, M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, no. 1, pp. 116–132, 1985.

    MATH  Google Scholar 

  2. S. Zhou, J. Lam, A. Xue. H ∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach. Fuzzy Sets and Systems, vol. 158, no. 2, pp. 180–193, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  3. Y. Y. Jun. H ∞ filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach. Fuzzy Sets and Systems, vol. 160, no. 12, pp. 1738–1748, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. H. Zhang, Y. Q. Xia, P. Shi, L. Wang. H ∞ fuzzy filtering for discrete-time nonlinear systems via fuzzy Lyapunov function approach. Circuits, Systems, and Signal Processing, vol. 28, no. 2 pp. 205–221, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Feng, M. Chen, D. Sun, T. J. Zhang. Approaches to robust filtering design of discrete time fuzzy dynamic systems. IEEE Transactions on Fuzzy Systems, vol. 16, no. 2, pp. 331–340, 2008.

    Article  Google Scholar 

  6. C. Lin, Q. G. Wang, T. H. Lee, B. Chen. H ∞ filter design for nonlinear systems with time-delay through T-S fuzzy model approach. IEEE Transactions of Fuzzy Systems, vol. 16, no. 3, pp. 739–746, 2008.

    Article  MathSciNet  Google Scholar 

  7. H. Zhang, S. Lun, D. Liu. Fuzzy H ∞ filter design for a class of nonlinear discrete-time systems with multiple time delays. IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 453–469, 2007.

    Article  Google Scholar 

  8. S. K. Nguang, P. Shi. Delay-dependent H ∞ filtering for uncertain time delay nonlinear systems: An LMI approach. IET Control Theory Applications, vol. 1, no. 1, pp. 133–140, 2007.

    Article  MathSciNet  Google Scholar 

  9. X. Li, X. P. Zhao, J. Chen. Controller design for electric power steering system using T-S fuzzy model approach. International Journal of Automation and Computing, vol.6, no. 2, pp. 198–203, 2009.

  10. M. Johansson, A. Rantzer, K. Arzen. Piecewise quadratic stability of fuzzy systems. IEEE Transactions on Fuzzy Systems, vol. 7, no. 6, pp. 713–722, 1999.

    Article  Google Scholar 

  11. M. Chen, G. Feng, H. B. Ma. A delay-dependent approach to H ∞ filtering for fuzzy time-varying delayed systems. In Proceedings of IEEE International Fuzzy Systems Conference, IEEE, London, UK, pp. 1–6, 2007.

    Google Scholar 

  12. C. L. Chen, H. X. Liu, X. P. Guan. H ∞ filtering of time-delay T-S fuzzy systems based on piecewise Lyapunov-Krasovskii functional. Signal Processing, vol. 89, no. 10, pp. 1998–2005, 2009.

    Article  MATH  Google Scholar 

  13. Z. Li, S. Y. Xu. Fuzzy weighting-dependent approach to robust L 2–L ∞ filter design for delayed fuzzy systems. Signal Processing, vol. 89, no. 4, pp. 463–571, 2009.

    Article  MATH  Google Scholar 

  14. C. Lin, Q. G. Wang, T. H. Lee, Y. He. Fuzzy weighting-dependent approach to H ∞ filter design for time-delay fuzzy systems. IEEE Transactions on Signal Processing, vol. 55, no. 6, pp. 2746–2751, 2007.

    Article  MathSciNet  Google Scholar 

  15. J. H. Zhang, Y. Q. Xia, R. Tao. New results on H ∞ filtering for fuzzy time-delay systems. IEEE Transactions on Fuzzy Systems, vol. 17, no. 1, pp. 128–137, 2009.

    Article  Google Scholar 

  16. A. Jadbabaie, C. T. Abdallah, D. Famularo, P. Dorato. Robust, non-fragile and optimal controller design via linear matrix inequalities. In Proceedings of the American Control Conference, IEEE, Philadelphia, Pennsylvania, USA, pp. 2482–2486, 1998.

    Google Scholar 

  17. L. H. Keel, S. P. Bhattacharyya. Robust, fragile, or optimal? IEEE Transactions on Automatic Control, vol. 42, no. 8, pp. 1098–1105, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  18. G. H. Yang, W. W. Che. Non-fragile H ∞ filter design for linear continuous-time systems. Automatica, vol. 44, no. 11, pp. 2849–2856, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  19. W. W. Che, G. H. Yang. Non-fragile H ∞ filtering for discrete-time systems with finite word length consideration Acta Automatica Sinica, vol. 34, no. 8, pp. 886–892, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  20. J.D. Chen, C. D. Yang, C.H. Lien, J. H. Horng. New delay-dependent non-fragile H ∞ observer-based control for continuous time-delay systems. Information Sciences, vol. 178, no. 24, pp. 4699–4706, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  21. W. J. Wang, Y. J. Chen, C. H. Sun. Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, vol. 37, no. 3, pp. 551–559, 2007.

    Article  MathSciNet  Google Scholar 

  22. Z. L. Xia, J. M. Li. GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function. International Journal of Automation and Computing, vol. 6, no. 3, pp. 271–276, 2009.

    Article  MathSciNet  Google Scholar 

  23. Z. L. Xia, J. M. Li. Delay-dependent H ∞ control for discrete-time fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function. Acta Automatica Sinica, vol. 35, no. 9, pp. 1235–1239, 2009.

    Article  MathSciNet  Google Scholar 

  24. Y. M. Li, S. Y. Xu, B. Y. Zhang, Y. M. Chu. Robust stabilization and H ∞ control for uncertain fuzzy neutral systems with mixed time delays. Fuzzy Sets and Systems, vol. 159, no. 20, pp. 2730–2748, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  25. G. L. Wei, G. Feng, Z. D. Wang. Robust H ∞ control for discrete-time fuzzy systems with infinite-distributed delays. IEEE Transactions on Fuzzy Systems, vol. 17, no. 1, pp. 224–232, 2009.

    Article  Google Scholar 

  26. J. H. Zhang, P. Shi, H. J. Yang. Non-fragile robust stabilization and H ∞ control for uncertain stochastic nonlinear time-delay systems. Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 3187–3196, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  27. C. L. Chen, G. Feng, X. P. Guan. Delay-dependent stability analysis and controller synthesis for discrete-time T-S fuzzy systems with time delays. IEEE Transactions on Fuzzy Systems, vol. 13, no. 5, pp. 630–643, 2005.

    Article  Google Scholar 

  28. C. Peng, Y. C. Tian, E. G. Tian. Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay. Fuzzy Sets and Systems, vol. 159, no. 20, pp. 2713–2729, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  29. L. Wu, P. Shi, C. Wang, H. Gao. Delay-dependent robust H ∞ and L 2−L ∞ filtering for LPV systems with both discrete and distributed delays. IEE Proceedings: Control Theory and Applications, vol. 153, no. 4, pp. 483–492, 2006.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Xidian University, Xi’an, 710071, PRC

    Zhi-Le Xia, Jun-Min Li & Jiang-Rong Li

  2. School of Mathematics and Information Engineering, Taizhou University, Taizhou, 317000, PRC

    Zhi-Le Xia

  3. College of Mathematics and Computer Science, Yanan University, Yanan, 716000, PRC

    Jiang-Rong Li

Authors
  1. Zhi-Le Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun-Min Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiang-Rong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Le Xia.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60974139, No. 60804021) and Fundamental Research Funds for the Central Universities.

Zhi-Le Xia received the B. Sc. degree in the Department of Mathematics at Huaiyin Normal University, Huaiyin, PRC in 2003, and the M. Sc. degree in the Department of Applied Mathematics at Xidian University, Xi’an, PRC in 2006. He is currently a Ph. D. candidate in the Department of Applied Mathematics at Xidian University, PRC. He is also a lecture of School of Mathematics and Information Engineering, Taizhou University, PRC.

His research interests include stochastic control, fuzzy control, and time-delay control systems.

Jun-Min Li received the B. Sc. and M. Sc. degrees from the Department of Applied Mathematics at Xidian University, PRC in 1987 and 1989, respectively, and Ph.D. degree in systems engineering from Xi’an Jiaotong University, Xi’an, PRC in 1997. He is currently a professor in the Department of Applied Mathematics at Xidian University, PRC.

His research interests include robust and adaptive control, optimal control, iterative learning control, and networked control systems.

Jiang-Rong Li received the B. Sc. degree in the Department of Mathematics at Shaanxi Normal University, Xi’an, PRC in 2001, and the M. Sc. degree in the Department of Applied Mathematics at Xidian University, Xi’an, PRC in 2006. She is currently a Ph. D. candidate in the Department of Applied Mathematics at Xidian University, PRC. She is also a lecture of College of Mathematics and Computer Science, Yanan University, PRC.

Her research interests include piecewise control, fuzzy control, and H 2 control.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xia, ZL., Li, JM. & Li, JR. Delay-dependent non-fragile H ∞ filtering for uncertain fuzzy systems based on switching fuzzy model and piecewise Lyapunov function. Int. J. Autom. Comput. 7, 428–437 (2010). https://doi.org/10.1007/s11633-010-0524-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-010-0524-6

Keywords