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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

On the Uniform Stabilization of Takagi-Sugeno Fuzzy Systems with Uncertainties

Journal of Applied Nonlinear Dynamics 8(4) (2019) 519--531 | DOI:10.5890/JAND.2019.12.001

Mohamed Ksantini$^{1}$, Mohamed Ali Hammami$^{2}$, Fran¸cois Delmotte$^{3}$

$^{1}$ University of Sfax, CEM Lab, Departement of Electrical Engineering, National School of Engineers of Sfax (ENIS), Tunisia

$^{2}$ University of Sfax, Tunisia

$^{3}$ University of Artois, France

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This paper studies the stabilization based controller problem for Takagi-Sugeno fuzzy nonlinear systems. We give some new conditions to prove the global uniform stability of the closed-loop fuzzy control systems in presence of uncertainties. Furthermore, a numerical example is treated to validate our approach.


  1. [1]  Takagi, T. and Sugeno, M. (1985), Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cyber., 15, 116-132,.
  2. [2]  Delmotte, F., Guerra, T.M., and Ksontini, M. (2007), Continuous Takagi-Sugeno’s Models: Reduction of the Number of LMI conditions in various fuzzy control design techniques, IEEE Trans. on Fuzzy Systems, 15(3), 426-438.
  3. [3]  Feng, G. (2006), A survey on analysis and design of model-based fuzzy control systems, IEEE Transactions on Fuzzy Systems, 14(5), 676-697.
  4. [4]  Guerra, T.M. and Vermeiren, L. (2004), LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugenos form, Automatica, 40(5), 823-829.
  5. [5]  HadjTaieb, N., Hammami, M.A., Delmotte, F., and Ksontini, M. (2012), On the global stabilization of Takagi-Sugeno fuzzy cascaded systems, Nonlinear Dynamics, 2847-2856.
  6. [6]  Fateh, M. and Amerian, M. (2013), Guaranteed-stability adaptive fuzzy control of a hydraulic elevator, International Journal of Intelligent Computing and Cybernetics, 6(3), 252-271.
  7. [7]  Ksantini, M., Delmotte, F., Guerra, T.M., and Kamoun, A. (2003), Disturbance rejection using Takagi- Sugeno fuzzy model applied to an interconnected tank system, International Conference on Systems, Man and Cybernetics, IEEE SMC’2003, 3352-3357, October 5-8(2003), Washington, D.C., USA.
  8. [8]  Lee, H.J., Park, J.B., and Chen, G. (2001), Robust fuzzy control of nonlinear systems with parameter uncertainties, IEEE Trans. Fuzzy Syst., 9(2), 369-379.
  9. [9]  Su, X., Shi, P., Wu, L., and Song, Y. (2013), A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays, IEEE Trans on Fuzzy Systems, 21(4), 655-671,.
  10. [10]  Su, X., Shi, P., Wu, L., and Nguang, S. (2013), Induced l2 filtering of fuzzy stochastic systems with timevarying delays, IEEE Trans on Cybernetics, 43(4), 1251-1264.
  11. [11]  Sugeno, M. and Kang, G.T. (1988), Structure identification of fuzzy model, Fuzzy Sets and Systems., 28, 15-33.
  12. [12]  Wang, H.O., Tanaka, K., and Grint, M. (1995), Parallel distributed compensation of nonlinear systems by Takagi and Sugeno’s model, Proceedings of FUZZIEE’95, 2.
  13. [13]  Wu, Z., Shi, P., Su, H., and Chu, J. (2014), Sampled-data fuzzy control of chaotic systems based on a T-S fuzzy model, IEEE Trans on Fuzzy Systems, 22(1), 153-163.
  14. [14]  Chang, W.J., Ku, C.C., and Chang, W. (2009), Fuzzy control with passivity synthesis for continuous affine Takagi-Sugeno fuzzy systems, International Journal of Intelligent Computing and Cybernetics, 2(2), 386-408.
  15. [15]  Zhou, Q., Shi, P., Xu, S., and Li, H. (2013), Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach, IEEE Trans on Fuzzy Systems, 21(2), 301-313.
  16. [16]  Corless, M. and Glielmo, L. (1992), On the exponential stability of singularly perturbed systems, SIAM J. Control and Optimisation, 30(6), 1338-1360.
  17. [17]  Hammami, M.A. (2001), On the stability of nonlinear control systems with uncertainty, Journal of Dynamical and Control Systems, 7(2), 171-179.
  18. [18]  Khalil, H.K. (2002), Nonlinear systems. 3rd ed., Englewood Cliffs, NJ: Prentice-Hall.
  19. [19]  Tanaka, K., Ikeda, T., and Wang, H.O. (1998), Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs, IEEE Transactions on Fuzzy Systems, 6(2), 250-265.
  20. [20]  Dong, J. and Yang, G.H. (2011), Control synthesis of T-S fuzzy systems based on a new control scheme, IEEE Transactions on Fuzzy Systems, 19(2), 323-338.
  21. [21]  Ben Makhlouf, A. and Hammami, M.A. (2014), A nonlinear inequality and application to global asymptotic stability of perturbed systems, Mathematical Methods in the Applied Sciences, 38(12), 2496-2505, DOI: 10.1002/mma.3236.
  22. [22]  Ksantini, M., Ellouze, A., and Delmotte, F. (2013), Control of a hydraulic system by means of a fuzzy approach, International Journal of Optimization and Control : Theories and Applications, IJOCTA, 3(2), 121-131.
  23. [23]  Ksantini, M., Hammami, M.A., and Delmotte, F. (2015), On the global exponential stabilization of Takagi- Sugeno fuzzy uncertain systems, Int. J. Innovative Comp. Inf. Contr., 11(1), 281-294.