Skip to main content
SpringerLink
Log in

Observer-based dissipative output feedback control for network T–S fuzzy systems under time delays with mismatch premise

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper deals with the problem of non-parallel distribution compensation networked control systems (NCSs) under event-triggered strategy based on the fuzzy system for a class of nonlinear systems with time-varying delays and mismatching premise membership functions. The T–S fuzzy model under event-triggered strategy is provided in unified framework, in which (1) a delay fuzzy observer-based with the mismatch premise is employed to approximate the immeasurable states of the existing system; (2) a delay fuzzy observer-based controller is constructed, by considering the same premises as in observer; and (3) event-triggered strategy is considered to mitigate the effect of communication burden. Another derivation of this paper is to introduce the notation of extended dissipativity which provides the \(H_{\infty }\), \(L_{2}-L_{\infty }\) and dissipative performances. Furthermore, in this regard, by taking into account a novel fuzzy Lyapunov–Krasovskii functional in conjunction with free weighting matrices, containing mode-dependent integral terms such that the resulting system is stable with the desired performance. Then, desired observer-based controller is presented in the account of LMI. Finally, we validate our results with a truck–trailer example.

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
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Chang, X.H., Yang, G.H.: Relaxed stabilization conditions for continuous-time Takagi–Sugeno fuzzy control systems. Inf. Sci. 180(17), 3273–87 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Xie, X.P., Liu, Z.W., Zhu, X.L.: An efficient approach for reducing the conservatism of LMI based stability conditions for continuous-time T–S fuzzy systems. Fuzzy Sets Syst. 263, 71–81 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Xie, X.P., Yue, D., Zhu, X.L.: Further studies on control synthesis of discrete-time T–S fuzzy systems via use ful matrix equalities. IEEE Trans. Fuzzy Syst. 22(4), 1026–31 (2014)

    Article  Google Scholar 

  4. Xie, X.P., Yue, D., Zhang, H.G., Xue, Y.S.: Control synthesis of discrete-time T–S fuzzy systems via a multi-instant homogenous polynomial approach. IEEE Transact. Cybern. (2015). https://doi.org/10.1109/TCYB.2015.2411336

  5. Fang, C.H., Liu, Y.S., Kau, S.W., Hong, L., Lee, C.H.: A new LMI based approach to relaxed quadratic stabilization of Takagi–Sugen of fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(3), 386–97 (2016)

    Article  Google Scholar 

  6. Dong, J.X., Yang, G.H., Zhang, H.G.: Stability analysis of T–S fuzzy control systems by using set theory. IEEE Transactions on Fuzzy and System (2014). https://doi.org/10.1109/TFUZZ.2014.2328016

  7. Chang, X.H.: Robust non fragile filtering of fuzzy systems with linear fractional parametric uncertainties. IEEE Trans. Fuzzy Syst. 20(6), 1001–11 (2012)

    Article  Google Scholar 

  8. Lam, H.K.: LMI based stability analysis for fuzzy model based control systems using artificial T–S fuzzy model. IEEE Trans. Fuzzy Syst. 19(3), 505–13 (2011)

    Article  Google Scholar 

  9. Lam, H.K., Narimani, M.: Quadratic stability analysis of fuzzy model based control systems using staircase membership functions. IEEE Trans. Fuzzy Syst. 18(1), 125–37 (2010)

    Article  Google Scholar 

  10. Lam, H.K., Narimani, M.: Stability analysis and performance deign for fuzzy model based control system under imperfect premise matching. IEEE Trans. Fuzzy Syst. 17(4), 949–61 (2009)

    Article  Google Scholar 

  11. Zhao, T., Dian, S.Y.: Delay dependent stabilization of discrete-time interval type-2 T–S fuzzy systems with time-varying delay. J. Franklin Inst. 354(3), 1542–67 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, J., Zha, L., Xie, X., Tian, E.: Resilient observer-based control for networked nonlinear T–S fuzzy systems with hybrid-triggered scheme. Nonlinear Dyn. https://doi.org/10.1007/s11071-017-4002-3, (2017)

  13. Tong, S.C., Wang, T., Li, Y.M., Zhang, H.G.: Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics. IEEE Trans. Cybern. 44(6), 910–921 (2014)

    Article  Google Scholar 

  14. Zhang, H.G., Wang, Z.S., Liu, D.R.: A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25(7), 1229–1262 (2014)

    Article  Google Scholar 

  15. Tian, E.G., Yue, D.: Reliable \(H_{\infty }\) filter design for T–S fuzzy modelbased networked control systems with random sensor failure. Int. J. Robust Nonlinear Control 23(1), 15–32 (2013)

    Article  MATH  Google Scholar 

  16. Peng, C., Yang, T.C.: Event-triggered communication and \(H_{\infty }\) control co-design for networked control systems. Automatica 49(5), 1326–1332 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu, Y.J., Tong, S.C.: Adaptive fuzzy identification and control for a class of nonlinear pure-feedback MIMO systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 23(5), 1387–1398 (2015)

    Article  Google Scholar 

  18. Zhang, H.G., Xie, X.P., Tong, S.C.: Homogenous polynomially parameter-dependent \(H_{\infty }\) filter designs of discrete-time fuzzy systems. IEEE Trans. Syst. Man Cybern. B 41(5), 1313–1322 (2011)

    Article  Google Scholar 

  19. Li, Y.M., Sui, S., Tong, S.C.: Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics. IEEE Trans. Cybern. 47(2), 403–414 (2017). https://doi.org/10.1109/TCYB.2016.2518300

    Google Scholar 

  20. Peng, C., Song, Y., Xie, X.P., Zhao, M., Fei, M.-R.: An event-triggered output tracking control for wireless networked control systems with communication delays and data dropouts. IET Control Theory Appl. 10(17), 2195–2203 (2016)

    Article  MathSciNet  Google Scholar 

  21. Li, H.Y., Chen, Z.R., Wu, L.G., Lam, H.K., Du, H.: Event-triggered fault detection of nonlinear networked systems. IEEE Trans. Cybern. https://doi.org/10.1109/TCYB.2016.2536750

  22. Peng, C., Han, Q.L., Yue, D.: To transmit or not to transmit: a discrete event-triggered communication scheme for networked Takagi–Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 21(1), 164–170 (2013)

    Article  Google Scholar 

  23. Yue, D., Tian, E.G., Han, Q.L.: A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. Autom. Control 58(2), 475–481 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  25. Asemani, M.H., Majd, V.J.: A robust \(H_{\infty }\) observer-based controller design for uncertain T–S fuzzy systems with unknown premise variables via LMI. Fuzzy Sets Syst. 212, 21–40 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. Nguang, S.K., Shi, P.: \(H_{\infty }\) fuzzy output feedback control design for nonlinear systems: an LMI approach. IEEE Trans. Fuzzy Syst. 11, 331–340 (2003)

    Article  Google Scholar 

  27. Besheer, A.H., Emara, H.M., Aziz, M.M.A.: Fuzzy-based output-feedback \(H_{\infty }\) control for uncertain nonlinear systems: an LMI approach. IET Control Theory Appl. 1, 1176–1185 (2007)

    Article  MathSciNet  Google Scholar 

  28. Zhao, T., Wei, Z., Dian, S., Xiao, J.: Observer-based \(H_{\infty }\) controller design for interval type-2 T–S fuzzy systems. Neurocomputing 177, 9–25 (2016)

    Article  Google Scholar 

  29. Zhang, B., Zheng, W.X., Xu, S.: Filtering of Markovian jump delay systems based on a new performance index. IEEE Trans. Circuits Syst. I: Regul. Pap. 60(5), 1250–1263 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  31. Peng, C., Yue, D., Fei, M.R.: Relaxed stability and stabilization conditions of networked fuzzy control systems subject to asynchronous grades of membership. IEEE Trans. Fuzzy Syst. 22(5), 1101–1112 (2014)

    Article  Google Scholar 

  32. Peng, C., Yang, T.C.: Communication-delay-distribution-dependent networked control for a class of T–S fuzzy systems. IEEE Trans. Fuzzy Syst. 18(2), 326–335 (2010)

    Google Scholar 

  33. Aslam, M.S., Chen, Z., Zhang, B.: Event-triggered fuzzy filtering in networked control system for a class of non-linear system with time delays. Int. J. Syst. Sci. (2018). https://doi.org/10.1080/00207721.2018.1463410

  34. Peng, C., Ma, S., Xie, X.: Observer-based non-PDC control for networked T–S fuzzy systems with an event-triggered communication. IEEE Trans. Cybern. 47(8), 2279–2287 (2017)

    Article  Google Scholar 

  35. Aslam, M.S., Zhang, B., Zhang, Y., Zhang, Z.: Extended dissipative filter design for T–S fuzzy systems with multiple time delays. ISA Trans. 80, 22–34 (2018)

    Article  Google Scholar 

  36. Tanaka, K., Sano, M.: A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck–trailer. IEEE Trans. Fuzzy Syst. 2(2), 119–134 (1994)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  38. Wu, H.N., Li, H.X.: New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay. IEEE Trans. Fuzzy Syst. 15(3), 482–493 (2007)

    Article  Google Scholar 

  39. Qiu, J., Feng, G., Yang, J., Sun, Y.: \(H_{\infty }\) filtering design for continuous-time nonlinear systems with interval time-varying delay via T–S fuzzy models. In: IEEE Proceedings of the 7th Asian Control Conference, Hong Kong, China (2009)

  40. Pan, Y., Yang, G.H.: Event-triggered fuzzy control for nonlinear networked control systems. Fuzzy Sets Ssyst. 329, 91–107 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Natural Science Fund for Distinguished Young Scholars of Jiangsu Province [Grant Number BK20150034].

Author information

Authors and Affiliations

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

    Muhammad Shamrooz Aslam & Ziran Chen

Authors
  1. Muhammad Shamrooz Aslam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ziran Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Shamrooz Aslam.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aslam, M.S., Chen, Z. Observer-based dissipative output feedback control for network T–S fuzzy systems under time delays with mismatch premise. Nonlinear Dyn 95, 2923–2941 (2019). https://doi.org/10.1007/s11071-018-4732-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-018-4732-x

Keywords

Search

Navigation