International Journal of Fuzzy Systems

, Volume 21, Issue 2, pp 571–582 | Cite as

Fuzzy PID Controller Design for Uncertain Networked Control Systems Based on T–S Fuzzy Model with Random Delays

  • Xinxin Lv
  • Juntao Fei
  • Yonghui SunEmail author


In this paper, the stochastic stabilization problem of uncertain networked control systems involving Takagi–Sugeno (T–S) fuzzy model, transmission delays and external disturbances is investigated, where the random network-induced delays are modeled as Markov chains. Firstly, by combining T–S fuzzy model with fuzzy PID controller, the uncertain networked control systems with random communication delays and external disturbances are modeled. Then, the uncertain networked control system is simplified through a mathematical method, and the stabilizing controller is derived for the uncertain networked control systems by using Lyapunov functional and linear matrix inequality. Finally, simulation results are presented to verify the effectiveness and availability of the developed results.


Fuzzy PID controller Uncertain networked control systems (UNCSs) Takagi–Sugeno (T–S) fuzzy model Transmission delay 



This work was supported in part by the National Natural Science Foundations of China under Grants 61374100 and 61673161, in part by the Natural Science Foundation of Jiangsu Province of China under Grant BK20161510 and in part by the Fundamental Research Funds for the Central Universities of China under Grant 2017B13914.


  1. 1.
    Wu, Y., Wu, Y.: Mode-dependent robust stability and stabilization of uncertain networked control systems via an average dwell time switching approach. IET Control Theory Appl. 11(11), 1726–1735 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Yang, F., Zhang, H.: TS model based relaxed reliable stabilization of networked control systems with time-varying delays under variable sampling. Int. J. Fuzzy Syst. 13(4), 260–269 (2011)MathSciNetGoogle Scholar
  3. 3.
    Peng, C., Tian, Y., Tade, M.: State feedback controller design of networked control systems with interval time-varying delay and nonlinearity. Int. J. Robust Nonlin. 18(12), 1285–1301 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Zhang, D., et al.: Robust fuzzy-model-based filtering for nonlinear networked systems with energy constraints. J. Franklin Inst. 354(4), 1957–1973 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Lu, R., Xu, Y., Zhang, R.: A new design of model predictive tracking control for networked control system under random packet loss and uncertainties. IEEE Trans. Ind. Electron. 63(11), 6999–7007 (2016)CrossRefGoogle Scholar
  6. 6.
    Ma, H., et al.: Nussbaum gain adaptive back stepping control of nonlinear strict-feedback systems with unmodeled dynamics and unknown dead-zone. Int. J. Robust. Nonlin. (2018). zbMATHGoogle Scholar
  7. 7.
    Zhang, W., Yu, L.: A robust control approach to stabilization of networked control systems with short time-varying delays. Acta Autom. Sin. 36(1), 87–91 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chen, Y., Fei, S., Li, Y.: Robust stabilization for uncertain saturated time-delay systems: a distributed-delay-dependent polytopic approach. IEEE Trans. Autom. Control 62(7), 3455–3460 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Zhang, Y., et al.: Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints. Appl. Math. Comput. 326, 16–32 (2018)MathSciNetGoogle Scholar
  10. 10.
    Ma, H., et al.: Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances. IEEE Trans. Syst. Man Cybern. Syst. (2018). Google Scholar
  11. 11.
    Chen, Y., et al.: Regional stabilization for discrete time-delay systems with actuator saturations via a delay-dependent polytopic approach. Autom. Control, IEEE Trans (2018). Google Scholar
  12. 12.
    Shen, H., Song, X., Wang, Z.: Robust fault-tolerant control of uncertain fractional-order systems against actuator faults. IET Control Theory Appl. 7(9), 1233–1241 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Liu, Y., Park, J., Guo, B.: Results on stability of linear systems with time varying delay. IET Control Theory Appl. 11(1), 129–134 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Sun, C., Wang, W., Lin, W.: Linear control and parallel distributed fuzzy control design for TS fuzzy time-delay system. Int. J. Fuzzy Syst. 9(4), 229–235 (2007)MathSciNetGoogle Scholar
  15. 15.
    Qi, W., Park, J., Cheng, J., Kao, Y.: Robust stabilization for nonlinear time-delay semi-Markovian jump systems via sliding mode control. IET Control Theory Appl. 11(10), 1504–1513 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Dong, S., et al.: Hidden–Markov-model-based asynchronous filter design of nonlinear Markov jump systems in continuous-time domain. Cybern, IEEE Trans (2018). Google Scholar
  17. 17.
    Dong, S., et al.: Asynchronous control of continuous-time nonlinear Markov jump systems subject to strict dissipativity. Autom. Control, IEEE Trans (2018). Google Scholar
  18. 18.
    Qiu, J., Feng, G., Gao, H.: Static-output-feedback H control of continuous-time TS fuzzy affine systems via piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 21(2), 245–261 (2012)CrossRefGoogle Scholar
  19. 19.
    Shi, Y., Yu, B.: Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54(7), 1668–1674 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Zhang, H., Shi, Y., Wang, J.: Observer-based tracking controller design for networked predictive control systems with uncertain Markov delays. Int. J. Control 86(10), 1824–1836 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Zhang, B., Xu, S.: Delay-dependent robust H control for uncertain discrete-time fuzzy systems with time-varying delays. IEEE Trans. Fuzzy Syst. 17(4), 809–823 (2009)CrossRefGoogle Scholar
  22. 22.
    Shen, M., Ye, D., Fei, S.: Robust H static output control of discrete Markov jump linear systems with norm bounded uncertainties. IET Control Theory Appl. 8(15), 1449–1455 (2014)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhang, L., Wang, J., Ge, Y., Wang, B.: Robust distributed model predictive control for uncertain networked control systems. IET Control Theory Appl. 8(17), 1843–1851 (2014)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Wang, T., et al.: Network-based fuzzy control for nonlinear industrial processes with predictive compensation strategy. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 2137–2147 (2016)CrossRefGoogle Scholar
  25. 25.
    Sun, Y., et al.: Robust stabilization and synchronization of nonlinear energy resource system via fuzzy control approach. Int. J. Fuzzy Syst. 14(2), 337–343 (2012)MathSciNetGoogle Scholar
  26. 26.
    Su, X., et al.: Event-triggered fuzzy control of nonlinear systems with its application to inverted pendulum systems. Automatica 94, 236–248 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Su, X., et al.: Fault detection filtering for nonlinear switched stochastic systems. IEEE Trans. Autom. Control 61(5), 1310–1315 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Wu, Z., et al.: Asynchronous dissipative control for fuzzy Markov jump systems. IEEE Trans. Cybern. 48(8), 2426–2436 (2018)CrossRefGoogle Scholar
  29. 29.
    Zhang, H., Yang, J., Su, C.: TS fuzzy-model-based robust H design for networked control systems with uncertainties. IEEE Trans. Ind. Informat. 3(4), 289–301 (2007)CrossRefGoogle Scholar
  30. 30.
    Lu, Q., Shi, P., Lam, H., Zhao, Y.: Interval type-2 fuzzy model predictive control of nonlinear networked control systems. IEEE Trans. Fuzzy Syst. 23(6), 2317–2328 (2015)CrossRefGoogle Scholar
  31. 31.
    Li, H., et al.: Stabilization and separation principle of networked control systems using the TS fuzzy model approach. IEEE Trans. Fuzzy Syst. 23(5), 1832–1843 (2015)CrossRefGoogle Scholar
  32. 32.
    Wang, L.: Automatic tuning of PID controllers using frequency sampling filters. IET Control Theory Appl. 11(7), 985–995 (2017)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Wu, C., et al.: A genetic-based design of auto-tuning fuzzy PID controllers. Int. J. Fuzzy Syst. 11(1), 49–58 (2009)MathSciNetGoogle Scholar
  34. 34.
    Dasgupta, S., et al.: Networked control of a large pressurized heavy water reactor (PHWR) with discrete proportional-integral-derivative (PID) controllers. IEEE Trans. Nucl. Sci. 60(5), 3879–3888 (2013)CrossRefGoogle Scholar
  35. 35.
    Xue, D., Liu, L., Pan, F.: Variable-order fuzzy fractional PID controllers for networked control systems. In: IEEE 10th Conference on Industrial Electronics and Applications (ICIEA), pp. 1438–1442. Auckland (2015)Google Scholar
  36. 36.
    Xie, G., Wang, L.: Stabilization of networked control systems with time-varying network-induced delay. In: IEEE 43rd Conference on Decision and Control (CDC), pp. 3551–3556. Nassau (2004)Google Scholar
  37. 37.
    Liu, J., Huang, Z., Zhang, J.: The dominant degree and disc theorem for the Schur complement of matrix. J. Appl. Math. Comput. 215(12), 4055–4066 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Yue, D., Han, Q., Peng, C.: State feedback controller design of networked control systems. IEEE Trans. Circuits Syst. II Exp. Briefs 51(11), 640–644 (2004)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Energy and Electrical EngineeringHohai UniversityNanjingChina
  2. 2.College of IOT EngineeringHohai UniversityChangzhouChina

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