Skip to main content
SpringerLink
Log in

A Novel Asymmetric Lyapunov–Krasovskii Functional Method to Stability for T–S Fuzzy Systems with Time-Varying Delay

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

Abstract

In this paper, a novel asymmetric Lyapunov–Krasovskii functional (LKF) method for the stability of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay is proposed. This asymmetric LKF method is shown to effectively reduce conservatism compared with symmetric LKF method. For further improving the stability criterion, the method is combined with the improved membership-function-dependent technique. Two numerical examples are given to demonstrate the advantages of our method and stability criterion numerically.

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

Fig. 1

Similar content being viewed by others

References

  1. Feng, Z.G., Zheng, W.X.: Improved stability condition for Takagi–Sugeno fuzzy systems with time-varying delay. IEEE Trans. Cyber. 47(3), 661–670 (2017)

    Article  Google Scholar 

  2. Li, Z.C., Yan, H.C., Zhang, H., Sun, J., Lam, H.-K.: Stability and stabilization with additive freedom for delayed Takagi–Sugeno fuzzy systems by intermediary-polynomial-based functions. IEEE Trans. Fuzzy Syst. 28(4), 692–705 (2020)

    Article  Google Scholar 

  3. Lian, Z., He, Y., Zhang, C.-K., Wu, M.: Stability and stabilization of T–S fuzzy systems with time-varying delays via delay-product-type functional method. IEEE Trans. Cyber. 50(6), 2580–2589 (2020)

    Article  Google Scholar 

  4. Lian, Z., He, Y., Wu, M.: Stability and stabilization for delayed fuzzy systems via reciprocally convex matrix inequality. Fuzzy Sets Syst. 402, 124–141 (2021)

    Article  MathSciNet  Google Scholar 

  5. Wang, G., Jia, L., Zhang, H.C.: Stability and stabilization of T–S fuzzy time-delay system via relaxed integral inequality and dynamic delay partition. IEEE Trans. Fuzzy Syst. 1, 1 (2020). https://doi.org/10.1109/TFUZZ.2020.3007416

    Article  Google Scholar 

  6. Wang, L.K., Lam, H.-K.: New stability criterion for continuous-time Takagi–Sugeno fuzzy systems with time-varying delay. IEEE Trans. Cyber. 49(4), 1551–1556 (2019)

    Article  Google Scholar 

  7. Tong, S.C., Li, T.M., Feng, G., Li, T.S.: Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems. IEEE Trans. Syst. Man Cybern. B 41(4), 1124–1135 (2011)

    Article  Google Scholar 

  8. Tong, S.C., Sui, S., Li, Y.M.: Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans. Fuzzy Syst. 23(4), 729–742 (2015)

    Article  Google Scholar 

  9. Wang, L.K., Lam, H.-K.: A new approach to stability and stabilization analysis for continuous-time Takagi–Sugeno fuzzy systems with time delay. IEEE Trans. Fuzzy Syst. 26(4), 2460–2465 (2018)

    Article  Google Scholar 

  10. Li, G.L., Peng, C., Fei, M.R., Tian, Y.C.: Local stability conditions for T–S fuzzy time-delay systems using a homogeneous polynomial approach. Fuzzy Sets Syst. 385, 111–126 (2020)

    Article  MathSciNet  Google Scholar 

  11. Zhang, Z.Y., Lin, C., Chen, B.: New stability and stabilization conditions for T–S fuzzy systems with time delay. Fuzzy Sets Syst. 263, 82–91 (2015)

    Article  MathSciNet  Google Scholar 

  12. Kwon, O.M., Park, M.J., Park, J.H., Lee, S.M.: Stability and stabilization of T–S fuzzy systems with time-varying delays via augmented Lyapunov–Krasovskii functionals. Inform. Sci. 372, 1–15 (2016)

    Article  MathSciNet  Google Scholar 

  13. Zhao, X., Lin, C., Chen, B., Wang, Q.-G.: A novel Lyapunov–Krasovskii functional approach to stability and stabilization for T–S fuzzy systems with time delay. Neurocomputing 313, 288–294 (2018)

    Article  Google Scholar 

  14. Sheng, Z.L., Lin, C., Chen, B., Wang, Q.-G.: Asymmetric LKF method on stability on stability of time-delay systems. Int. J. Robust Nonlinear Control 31(7), 2847–2854 (2021)

    Article  Google Scholar 

  15. Sheng, Z.L., Lin, C., Chen, B., Wang, Q.G.: An asymmetric Lyapunov–Krasovskii functional method on stability and stabilization for T–S fuzzy systems with time delay. IEEE Trans. Fuzzy Syst. 1, 1 (2021)

    Article  Google Scholar 

  16. Gu, K., Kharitonov, V.-L., Chen, J.: Stability of Time-Delay Systems. Birkhauser, Basel (2003)

    Book  Google Scholar 

  17. Seuret, A., Gouaisbaut, F.: Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9), 2860–2866 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. Zhang, C.-K., He, Y., Jiang, L., Wu, M., Wang, Q.-G.: An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay. Automatica 85, 481–485 (2017)

    Article  MathSciNet  Google Scholar 

  20. Chen, P., Fei, M.-R.: An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay. Fuzzy Sets Syst. 12, 97–109 (2013)

    MathSciNet  MATH  Google Scholar 

  21. Souza, F.O., Campos, V.C.S., Palhares, R.M.: On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems. J. Frankl. Inst. 351(7), 3707–3718 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported in part by the National Natural Science Foundation of China under Grant 61673227, Grant 61873137, and the Shandong Taishan Scholar Project (No. ts20190930)

Author information

Authors and Affiliations

  1. Institute of Complexity Science, Shandong Key Laboratory of Industrial Control Technology, The School of Automation, Qingdao University, Qingdao, 266071, China

    Zhaoliang Sheng, Chong Lin & Bing Chen

  2. School of Artificial Intelligence, Hebei University of Technology, Tianjin, 300401, China

    Likui Wang

Authors
  1. Zhaoliang Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Likui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chong Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. 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

Sheng, Z., Wang, L., Lin, C. et al. A Novel Asymmetric Lyapunov–Krasovskii Functional Method to Stability for T–S Fuzzy Systems with Time-Varying Delay. Int. J. Fuzzy Syst. 24, 949–956 (2022). https://doi.org/10.1007/s40815-021-01176-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-021-01176-w

Keywords

Search

Navigation