Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 175–198 | Cite as

Robust \( H_{\infty } \) Fault-Tolerant Control for Discrete-Time Nonlinear System with Actuator Faults and Time-Varying Delays Using Nonlinear T–S Fuzzy Models

  • Djamel Eddine CheridiEmail author
  • Noura Mansouri


In this paper, the problem of fault estimation and fault-tolerant control for a class of nonlinear discrete-time system state time-varying delay and actuator fault is investigated. This class of systems is represented through the Takagi–Sugeno (T–S) fuzzy model with nonlinear functions satisfying some sector-bounded conditions. By adding these nonlinear functions in the local sub-models, the observer and controller can be designed with fewer rules and less computation burden. The method proceeds in two steps: first, a full-order fuzzy fault estimation observer (FFEO) design is proposed to estimate the actuator faults and the nonlinear functions in the T–S models. Second, based on the online fault estimation, a dynamic output feedback fault-tolerant controller (DOFTC) is then designed to compensate the effect of faults by stabilizing the closed-loop system. Furthermore, sufficient less conservative delay-dependent conditions for the existence of the desired FFEO and DOFTC are given in terms of linear matrix inequalities by employing the fuzzy Lyapunov–Krasovskii function and free-weighting approach. Finally, a practical example is given to show the effectiveness and advantages of the proposed approach.


Discrete-time systems Fault-tolerant control T–S fuzzy systems Fuzzy estimator \( \varvec{H}_{\infty } \varvec{ } \) control 



  1. 1.
    S. Abdelmalek, M.A. Azar, D. Dib, A novel actuator fault-tolerant control strategy of DFIG-based wind turbines using Takagi–Sugeno multiple models. Int. J. Control Autom. Syst. 16(3), 1415–1424 (2018)CrossRefGoogle Scholar
  2. 2.
    W. Assawinchaichote, S.K. Nguang, P. Shi, Fuzzy Control and Filter Design for Uncertain Fuzzy Systems (Springer, Berlin, 2006)zbMATHGoogle Scholar
  3. 3.
    M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and Fault-Tolerant Control (Springer, Berlin, 2006)zbMATHGoogle Scholar
  4. 4.
    J. Cheng, J.H. Park, J. Cao, D. Zhang, Quantized H filtering for switched linear parameter-varying systems with sojourn probabilities and unreliable communication channels. Inf. Sci. 466, 289–302 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    D.E. Cheridi, N. Mansouri, H fault estimation for nonlinear discrete time-delay system with actuator and sensor faults using nonlinear T–S fuzzy models, in 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B), (IEEE, 2017), pp. 1–6Google Scholar
  6. 6.
    H. Dong, Z. Wang, D.W.C. Ho, H. Gao, Robust H fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements. IEEE Trans. Fuzzy Syst. 18(4), 712–725 (2010)CrossRefGoogle Scholar
  7. 7.
    H. Dong, Z. Wang, J. Lam, H. Gao, Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts. IEEE Trans. Syst. Man Cybern. Part B Cybern. 42(2), 365–376 (2011)CrossRefGoogle Scholar
  8. 8.
    H. Gassara, A. El Hajjaji, M. Chaabane, Robust control of T–S fuzzy systems with time-varying delay using new approach. Int. J. Robust Nonlinear Control 20, 1566–1578 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    S. Ghorbel, A. El Hajjaji, M. Souissi, M. Chaabane, Fault-tolerant trajectory tracking control for Takagi–Sugeno systems with unmeasurable premise variables: descriptor approach. Circuits Syst. Signal Process. 33(6), 1763–1781 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    T.M. Guerra, A. Kruszewski, J. Lauber, Discrete Tagaki-Sugeno models for control: where are we? Ann. Rev. Control 33(1), 37–47 (2009)CrossRefGoogle Scholar
  11. 11.
    Li-Y Hao, JuH Park, D. Ye, Integral sliding mode fault-tolerant control for uncertain linear systems over networks with signals quantization. IEEE Trans. Cybern. 28(9), 2088–2100 (2017)MathSciNetGoogle Scholar
  12. 12.
    S. Huang, G. Yang, Fault tolerant controller design for T–S fuzzy systems with time-varying delay and actuator faults: a k-step fault-estimation approach. IEEE Trans. Fuzzy Syst. 22(6), 1526–1540 (2014)CrossRefGoogle Scholar
  13. 13.
    H. Inseok, K. Sungwan, K. Youdan, S. Chze Eng, A survey of fault detection, isolation, and reconfiguration methods. IEEE Trans. Control Syst. Technol. 18(3), 636–653 (2010)CrossRefGoogle Scholar
  14. 14.
    A. Jaballi, A.E. Hajjaji, A. Sakly, Reducing conservativeness of stabilization conditions for switched T–S fuzzy systems. Neurocomputing 193, 51–57 (2016)CrossRefGoogle Scholar
  15. 15.
    M.G. Kazemi, M. Montazeri, Robust fault detection of uncertain Lipschitz nonlinear systems with simultaneous disturbance attenuation level and enhanced fault sensitivity and Lipschitz constant. Circuits Syst. Signal Process. 37(10), 4256–4278 (2018)MathSciNetCrossRefGoogle Scholar
  16. 16.
    D. Kharrat, H. Gassara, A. El Hajjaji, M. Chaabane, Adaptive fuzzy observer-based fault-tolerant control for Takagi–Sugeno descriptor nonlinear systems with time delay. Circuits Syst. Signal Process. 37(4), 1542–1561 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    M. Klug, E.B. Castelan, V.J.S. Leite, L.F.P. Silva, Fuzzy dynamic output feedback control through nonlinear Takagi Sugeno models. Fuzzy Sets Syst. 263, 92–111 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    C. Lin, Q.-G. Wang, T.H. Lee, Y. He, LMI Approach to Analysis and Control of Takagi–Sugeno Fuzzy Systems with Time Delay (Springer, Berlin, 2007)zbMATHGoogle Scholar
  19. 19.
    J. Lofberg, YALMIP: a toolbox for modeling and optimization in MATLAB, in Proceedings of the CACSD conference, Taipei, Taiwan. pp. 284–289.
  20. 20.
    Y. Long, JuH Park, D. Ye, Transmission-dependent fault detection and isolation strategy for networked systems under finite capacity channels. IEEE Trans. Cybern. 47(8), 2268–2278 (2017)CrossRefGoogle Scholar
  21. 21.
    D.S. Niculescu, Delay Effects on Stability: A Robust Control Approach (Springer, Berlin, 2001)zbMATHGoogle Scholar
  22. 22.
    H. Noura, D. Theilliol, J.-C. Ponsart, A. Chamseddine, Fault-Tolerant Control Systems: Design and Practical Applications (Springer, London, 2009)zbMATHCrossRefGoogle Scholar
  23. 23.
    T.G. Park, Estimation strategies for fault isolation of linear systems with disturbances. IET Control Theory Appl. 4(12), 2781–2792 (2010)MathSciNetCrossRefGoogle Scholar
  24. 24.
    J. Qiu, Y. Wei, H.R. Karimi, H. Gao, Reliable control of discrete-time piecewise-affine time-delay systems via output feedback. IEEE Trans. Reliab. 67(1), 79–91 (2017)CrossRefGoogle Scholar
  25. 25.
    R. Sakthivel, P. Selvaraj, K. Mathiyalagan, JuH Park, Robust fault-tolerant H control for offshore steel jacket platforms via sampled-data approach. J. Frankl. Inst. 352(6), 2259–2279 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    P. Shi, S.X. Ding, Delay-dependent fault estimation for uncertain time-delay nonlinear systems: an LMI approach. Int. J. Robust Nonlinear Control 16(18), 913–933 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    X. Su, P. Shi, L. Wu, Y.D. Song, A novel control design on discrete-time Takagi–Sugeno fuzzy systems with time-varying delays. IEEE Trans. Fuzzy Syst. 2013(21), 655–671 (2012)Google Scholar
  28. 28.
    C. Sun, F. Wang, X. He, Robust fault estimation for Takagi–Sugeno nonlinear systems with time-varying state delay. Circuits Syst. Signal Process. 34, 641–661 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    K. Tanaka, H.O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (Wiley, New York, 2001)CrossRefGoogle Scholar
  30. 30.
    B. Wang, D. Zhang, J. Cheng, JuH Park, Fuzzy model-based nonfragile control of switched discrete-time systems. Nonlinear Dyn. 93(4), 2461–2471 (2018)zbMATHCrossRefGoogle Scholar
  31. 31.
    M. Xiang, Z. Xiang, Robust fault detection for switched positive linear systems with time-varying delays. ISA Trans. 53, 10–16 (2014)CrossRefGoogle Scholar
  32. 32.
    S. Xu, G. Feng, Y. Zou, J. Huang, Robust controller design of uncertain discrete time-delay systems with input saturation and disturbances. IEEE Trans. Autom. Control 57, 2604–2609 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    J. Yoneyama, H output feedback control for fuzzy systems with immeasurable premise variables: discrete-time case. Appl. Soft Comput. 8, 949–958 (2008)CrossRefGoogle Scholar
  34. 34.
    K. Zhang, B. Jiang, V. Cocquempot, H. Zhang, A framework of robust fault estimation observer design for continuous-time/discrete-time systems. Optim. Control Appl. 34, 442–457 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    K. Zhang, B. Jiang, P. Shi, Observer-Based Fault Estimation and Accomodation for Dynamic Systems (Springer, Berlin, 2013)CrossRefGoogle Scholar
  36. 36.
    K. Zhang, B. Jiang, M. Staroswiecki, Dynamic output feedback-fault tolerant controller design for Takagi–Sugeno fuzzy systems with actuator faults. IEEE Trans. Fuzzy Syst. 18(1), 194–201 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of ElectronicsFrères Mentouri UniversityConstantine CityAlgeria

Personalised recommendations