Skip to main content
SpringerLink
Log in

Delay-Dependent Nonfragile Robust H ∞ Filtering of T–S Fuzzy Time-Delay Systems

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

The problem of nonfragile robust H ∞ filtering for a class of Takagi–Sugeno fuzzy time-delay systems is investigated in the paper. We design a fuzzy filter which can tolerate some level of the filter gain variations while ensuring both the robust stability and a prescribed H ∞ performance level of the filtering error system. Delay-dependent sufficient conditions for the existence of such filters are obtained in terms of linear matrix inequalities, and an explicit expression of a desired filter is given.

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. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. SIAM Studies in Applied Mathematics (SIAM, Philadelphia, 1994)

    Google Scholar 

  2. Y.-Y. Cao, P.M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy Sets Syst. 124, 213–229 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Chen, X. Liu, Delay-dependent robust H ∞ control for T–S fuzzy systems with time delay. Fuzzy Sets Syst. 13, 544–556 (2005)

    Google Scholar 

  4. B. Chen, X. Liu, S. Tong, New delay-dependent stabilization conditions of T–S fuzzy systems with constant delay. Fuzzy Sets Syst. 158, 2209–2224 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Feng, C.L. Chen, D. Sun, X.P. Guan, H ∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov function and bilinear matrix inequalities. IEEE Trans. Fuzzy Syst. 13, 94–103 (2005)

    Article  Google Scholar 

  6. A. Jadbabaie, C.T. Abdallah, D. Famularo, P. Dorato, Robust, non-fragile and optimal controller design via linear matrix inequalities, in Proc. American Control Conference (Philadelphia, PA, 1998), pp. 2842–2846

  7. S.-W. Kau, H.-J. Lee, C.-M. Yang, C.-H. Lee, L. Hong, C.-H. Fang, Robust H ∞ fuzzy static output feedback control of T–S fuzzy systems with parametric uncertainties. Fuzzy Sets Syst. 158, 135–146 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. L.H. Keel, S.P. Bhattacharyya, Robust, fragile, or optimal? IEEE Trans. Automat. Control 42, 1098–1105 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. L.H. Keel, S.P. Bhattacharyya, Stability margins and digital implementation of controllers, in Proc. American Control Conference (1998), pp. 2852–2856

  10. J. Lam, S. Zhou, Dynamic output feedback H ∞ control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach. Int. J. Syst. Sci. 38, 25–37 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. K.R. Lee, E.T. Jeung, H.B. Park, Robust fuzzy H ∞ control for uncertain nonlinear systems via state feedback: an LMI approach. Fuzzy Sets Syst. 120, 123–134 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Y.-C. Lin, J.-C. Lo, Robust mixed H 2/H ∞ filtering for time-delay fuzzy systems. IEEE Trans. Signal Process. 54, 2897–2909 (1999)

    Article  Google Scholar 

  13. C. Lin, Q.G. Wang, T. Lee, Delay-dependent LMI conditions for stability and stabilization of T–S fuzzy systems with bounded time-delay. Fuzzy Sets Syst. 157, 1229–1247 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. C. Lin, Q.G. Wang, T. Lee, Y. He, Fuzzy weighting-dependent approach to H ∞ filter design for time-delay fuzzy systems. IEEE Trans. Signal Process. 55, 2746–2751 (2007)

    Article  MathSciNet  Google Scholar 

  15. M.S. Mahmoud, Resilient linear filtering of uncertain systems. Automatica 40, 1797–1802 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. S.K. Nguang, P. Shi, H ∞ fuzzy output feedback control design for nonlinear systems: An LMI approach. IEEE Trans. Fuzzy Syst. 11, 331–340 (2003)

    Article  Google Scholar 

  17. T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modelling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)

    MATH  Google Scholar 

  18. K. Tanaka, M. Sano, A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer. IEEE Trans. Fuzzy Syst. 2, 119–133 (1994)

    Article  Google Scholar 

  19. L. Xie, C.E. de Souza, Robust H ∞ control for linear systems with norm-bounded time-varying uncertainty. IEEE Trans. Automat. Control 37, 1188–1191 (1992)

    Article  MathSciNet  Google Scholar 

  20. S. Xu, J. Lam, B. Chen, Robust H ∞ control for uncertain fuzzy neutral delay systems. Eur. J. Control 10, 365–380 (2004)

    Article  MathSciNet  Google Scholar 

  21. S. Xu, J. Lam, T. Chen, Y. Zou, A delay-dependent approach to robust H ∞ filtering for uncertain distributed delay systems. IEEE Trans. Signal Process. 53, 3764–3772 (2005)

    Article  MathSciNet  Google Scholar 

  22. G.-H. Yang, W.-W. Che, Non-fragile H ∞ filter design with additive gain variations, in Proc. of the 45th IEEE Conf. Decision and Control (San Diego, CA, USA, 2006), pp. 4775–4780

  23. G.-H. Yang, J.L. Wang, Robust non-fragile Kalman filtering for uncertain linear systems. IEEE Trans. Automat. Control 46, 343–348 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  24. S. Zhou, T. Li, Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov–Kasovskii function. Fuzzy Sets Syst. 151, 139–153 (2005)

    Article  MATH  Google Scholar 

  25. S. Zhou, J. Lam, A. Xue, H ∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach. Fuzzy Sets Syst. 158, 180–193 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Ze Li & Shengyuan Xu

  2. Department of Mathematics, Huzhou Teacher’s College, Huzhou, Zhejiang, 313000, People’s Republic of China

    Yuming Chu

Authors
  1. Ze Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuming Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shengyuan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shengyuan Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Z., Chu, Y. & Xu, S. Delay-Dependent Nonfragile Robust H ∞ Filtering of T–S Fuzzy Time-Delay Systems. Circuits Syst Signal Process 29, 361–375 (2010). https://doi.org/10.1007/s00034-010-9148-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-010-9148-x

Keywords

Search

Navigation