Skip to main content
SpringerLink
Log in

New Results on \(H_{\infty }\) filter Design for Nonlinear Time-Delay Systems Via Fuzzy Line-Integral Approach

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper revisits the problem of \(H_{\infty }\) filtering design for nonlinear systems with time-varying delay through Takagi–Sugeno (T–S) fuzzy models. By applying the fuzzy line-integral Lyapunov function, a new sufficient condition for the existence of the fuzzy \(H_{\infty }\) filter design is established in terms of linear matrix inequalities. The present method provides improvements and produces better results than existing ones in the literature. Two examples are given to show the advantages and effectiveness of the proposed results.

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. Yang, F., Wang, Z., Hung, Y.S.: Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises. IEEE Trans. Autom. Control. 47(7), 1179–1183 (2002)

    Article  MathSciNet  Google Scholar 

  2. Simon, D.: Kalman filtering for fuzzy discrete time dynamic systems. Appl. Soft Comput. 3(3), 191–207 (2003)

    Article  Google Scholar 

  3. Gao, H.J., Wang, C.H.: Delay-dependent robust \(H_{\infty }\) and \(L_2\)-\(L_{\infty }\) filtering for a class of uncertain nonlinear time-delay systems. IEEE Trans. Autom. Control. 48(9), 1661–1666 (2003)

    Article  Google Scholar 

  4. Xu, S., Chen, T.: Robust \(H_{\infty }\) filtering for a class of nonlinear systems with state delay and parameter uncertainty. Int. J. Control. 75(10), 766–774 (2002)

    Article  MATH  Google Scholar 

  5. Zhang, H.S., Zhang, D., Xie, L.H., Lin, J.: Robust filtering under stochastic parametric uncertainties. Automatica 40(9), 1583–1589 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fridman, E., Shaked, U.: An improved delay-dependent \(H_{\infty }\) filtering of linear neutral systems. IEEE Trans. Signal Process. 52(3), 668–673 (2004)

    Article  MathSciNet  Google Scholar 

  7. Lin, C., Wang, Q.G., Lee, T.H., He, Y.: Fuzzy weighting-dependent approach to \(H_{\infty }\) filter design for time-delay fuzzy system. IEEE Trans. Signal Process. 55(6), 2746–2751 (2007)

    Article  MathSciNet  Google Scholar 

  8. Lin, C., Wang, Q.G., Lee, T.H., Chen, B.: \(H_{\infty }\) filter design for nonlinear systems with time-delay through T-S fuzzy model approach. IEEE Trans. Fuzzy Syst. 16(3), 739–745 (2008)

    Article  MathSciNet  Google Scholar 

  9. Su, Y.K., Chen, B., Lin, C., Zhang, H.G.: A new fuzzy \(H_{\infty }\) filter design for nonlinear continuous-time dynamic systems with time-varying delays. Fuzzy Sets Syst. 160(24), 3539–3549 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang, J.H., Xia, Y.Q., Tao, R.: New results on \(H_{\infty }\) filtering for fuzzy time-delay systems. IEEE Trans. Fuzzy Syst. 17(1), 128–137 (2009)

    Article  Google Scholar 

  11. Huang, S.J., He, X.Q., Zhang, N.N.: New results on \(H_{\infty }\) filter design for nonlinear systems with time delay via T-S fuzzy models. IEEE Trans. Fuzzy Syst. 19(1), 193–199 (2011)

    Article  Google Scholar 

  12. An, J., Wen, G., Lin, C., Li, R.: New results on a delay-derivative-dependent fuzzy \(H_{\infty }\) filter design for TCS fuzzy systems. IEEE Trans. Fuzzy Syst. 19(4), 770–779 (2011)

    Article  Google Scholar 

  13. Zhao, Y., Gao, H., Lam, J.: New results on \(H_{\infty }\) filtering for fuzzy systems with interval time-varying delays. Inf. Sci. 181(11), 2356–2369 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wu, H.N., Wang, J.W., Shi, P.: A delay decomposition approach to \(L_2-L_{\infty }\) filter design for stochastic systems with time-varying delay. Automatica 47(7), 1482–1488 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Liu, J.L., Gu, Z., Tian, E.G., Yan, R.X.: New results on \(H_{\infty }\) filter design for nonlinear systems with time-delay through a T-S fuzzy model approach. Int. J. Syst. Sci. 43(3), 426–442 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ding, D.W., Li, X.L., Wang, Y.Y., Shi, Z.G.: Non-fragile \(H_{\infty }\) fuzzy filtering for discrete-time non-linear systems. IET Control Theory Appl. 7(6), 848–857 (2013)

    Article  MathSciNet  Google Scholar 

  17. Zhang, H.B., Yu, G.J., Zhou, C.H., Dang, C.Y.: Delay-dependent decentralised \(H_{\infty }\) filtering for fuzzy interconnected systems with time-varying delay based on Takagi-Sugeno fuzzy model. IET Control Theory Appl. 7(5), 720–729 (2013)

    Article  MathSciNet  Google Scholar 

  18. Zhang, Z., Lin, C., Chen, B.: New decentralized \(H_{\infty }\) filter design for nonlinear interconnected systems based on Takagi-Sugeno fuzzy models. IEEE Trans. Cybern. 45(12), 2914–2924 (2015)

    Article  Google Scholar 

  19. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Syst. Man. Cybern. 15(1), 116–132 (1985)

    Article  MATH  Google Scholar 

  20. Tanaka, K., Wang, H.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, NewYork (2001)

    Book  Google Scholar 

  21. Feng, G.: A survey on analysis and design of model-based fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(5), 676–697 (2006)

    Article  Google Scholar 

  22. Zeng, H.B., Park, J.H., Xia, J.W., Xiao, S.P.: Improved delay-dependent stability criteria for T-S fuzzy systems with time-varying delay. Appl. Math. Comput. 235, 492–501 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tanaka, K., Hori, T., Wang, H.O.: A multiple Lyapunov function approach to stabilization of fuzzy control systems. IEEE Trans. Fuzzy Syst. 11(4), 582–589 (2003)

    Article  Google Scholar 

  24. Tanaka, K., Ohtake, H., Wang, H.O.: A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions. IEEE Trans. Fuzzy Syst. 15(3), 333–341 (2007)

    Article  Google Scholar 

  25. Mozelli, L.A., Palhares, R.M., Souza, F.O., Mendes, E.M.A.M.: Reducing conservativeness in recent stability conditions of TS fuzzy systems. Automatica 45(6), 1580–1583 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Lin, C., Wang, Q.G., Lee, T.H., He, Y.: Stability conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach. IET Control Theory Appl. 1(1), 127–132 (2007)

    Article  MathSciNet  Google Scholar 

  27. Lin, C., Wang, Q.G., Lee, T.H., He, Y.: LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems with Time Delay. Springer-Verlag, New York (2007)

    MATH  Google Scholar 

  28. Rhee, B.J., Won, S.: A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design. Fuzzy Sets Syst. 157(9), 1211–1228 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Tognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D.: Reduced-order dynamic output feedback control of continuous-time T-S fuzzy systems. Fuzzy Sets Syst. 207(16), 27–44 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  30. Campos, V.C.S., Souza, F.O., Tôrres, L.A.B., Palhares, R.M.: New stability conditions based on piecewise fuzzy Lyapunov functions and tensor product transformations. IEEE Trans. Fuzzy Syst. 21(4), 748–760 (2013)

    Article  Google Scholar 

  31. Guelton, K., Guerra, T.M., Bernal, M., ouarar, T.B., Manamanni, N.: Comments on fuzzy control systems design via fuzzy Lyapunov functions. IEEE Trans. Syst. Man Cybern. B 40(3), 970–972 (2010)

    Article  Google Scholar 

  32. Lo, J.C., Zhang, C.M.: Relaxation analysis via line integral. In: Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, pp. 1264–1269 (2009)

  33. Li, H., Pan, Y., Zhou, Q.: Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2015)

    Article  Google Scholar 

  34. Su, X., Shi, P., Wu, L., Nguang, S.K.: Induced \(l_2\) filtering of fuzzy stochastic systems with time-varying delays. IEEE Trans. Cybern. 43(4), 1251–1264 (2013)

    Article  Google Scholar 

  35. Su, X., Shi, P., Wu, L., Basin, M.V.: Reliable filtering with strict dissipativity for T-S fuzzy time-delay systems. IEEE Trans. Cybern. 44(12), 2470–2483 (2014)

    Article  Google Scholar 

  36. Su, X., Wu, L., Shi, P.: Sensor networks with random link failures: distributed filtering for T-S fuzzy systems. IEEE Trans. Ind. Inf. 9(3), 1739–1750 (2013)

    Article  Google Scholar 

  37. Park, P., Ko, J.W., Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1), 235–238 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  38. Gu, K., Kharitonov, V.L., Chen, J.: Stability of Time-Delay Systems. Springer-Verlag, Berlin (2003)

    Book  MATH  Google Scholar 

  39. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Upper Saddle River (2002)

    MATH  Google Scholar 

  40. Zill, D.G., Cullen, M.R.: Advanced Engineering Mathematics, 2nd edn. Jones and Bartlett, London (2000)

    MATH  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (61174033, 61473160, 61473178, 61503222) and in part by the Natural Science Foundation of Shandong Province, China (ZR2011FM006).

Author information

Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Ziye Zhang

  2. Institute of Complexity Science, Qingdao University, Qingdao, 266071, People’s Republic of China

    Ziye Zhang, Chong Lin & Bing Chen

Authors
  1. Ziye Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chong Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chong Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Lin, C. & Chen, B. New Results on \(H_{\infty }\) filter Design for Nonlinear Time-Delay Systems Via Fuzzy Line-Integral Approach. Int. J. Fuzzy Syst. 18, 904–913 (2016). https://doi.org/10.1007/s40815-015-0126-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-015-0126-0

Keywords

Search

Navigation