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Relaxed Stabilization Conditions for the T–S Fuzzy System with Input Constraints

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Abstract

The stabilization conditions of the discrete Takagi–Sugeno (T–S) fuzzy system are reduced by considering possible switching subregions. In addition, the stabilization conditions for the T–S fuzzy system are relaxed by representing the interactions among the fuzzy subsystems in a single matrix. However, these two concepts have not been applied together to the discrete T–S fuzzy system with constraints on the control input. The aim of this paper is to relax the stabilization conditions for the discrete T–S fuzzy system with constraints on the control input. The possible switching subregions fired by two successive states of the system are analyzed and utilized to reduce the stabilization conditions. The interactions of fuzzy subsystems within two subregions are integrated into a single matrix to relax the stabilization conditions. The relaxation and effectiveness of the proposed stabilization conditions are demonstrated by a numerical example and a mass-spring-damper system.

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References

  1. Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2001)

    Book  Google Scholar 

  2. Feng, G.: A survey on analysis and design of model-based fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(5), 676–697 (2006)

    Article  Google Scholar 

  3. Wang, W.Y., Chen, M.C., Su, S.F.: Hierarchical T–S fuzzy-neural control of anti-lock braking system and active suspension in a vehicle. Automatica 48(8), 1698–1706 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lian, K.Y., Hong, C.W.: Current-sensorless flyback converters using integral T–S fuzzy approach. Int. J. Fuzzy Syst. 15(1), 66–74 (2013)

    MathSciNet  Google Scholar 

  5. Lam, H.K., Lo, J.C.: Output regulation of polynomial-fuzzy-model-based control systems. IEEE Trans. Fuzzy Syst. 21(2), 262–274 (2013)

    Article  Google Scholar 

  6. Li, H., Jing, X., Lam, H.K., Shi, P.: Fuzzy sampled-data control for uncertain vehicle suspension systems. IEEE Trans. Cybern. 44(7), 1111–1126 (2014)

    Article  Google Scholar 

  7. Chen, Y.J., Tanaka, M., Tanaka, K., Ohtake, H., Wang, H.O.: Discrete polynomial fuzzy systems control. IET Control Theory Appl. 8(4), 288–296 (2014)

    Article  MathSciNet  Google Scholar 

  8. Cao, K., Gao, X., Lam, H.K., Vasilakos, A., Pedrycz, W.: A new relaxed stability condition for Takagi–Sugeno fuzzy control systems using quadratic fuzzy Lyapunov functions and staircase membership functions. Int. J. Fuzzy Syst. 16(3), 327–337 (2014)

    MathSciNet  Google Scholar 

  9. Lam, H.K., Wu, L., Lam, J.: Two-step stability analysis for general polynomial-fuzzy—model-based control systems. IEEE Trans. Fuzzy Syst. 23(3), 511–524 (2015)

    Article  Google Scholar 

  10. Chen, Y.J., Tanaka, M., Tanaka, K., Wang, H.O.: Stability analysis and region-of- attraction estimation using piecewise polynomial Lyapunov functions: polynomial fuzzy model approach. IEEE Trans. Fuzzy Syst. 23(4), 1314–1322 (2015)

    Article  Google Scholar 

  11. Wang, H.O., Tanaka, K., Griffin, M.F.: An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans. Fuzzy Syst. 4(1), 14–23 (1996)

    Article  Google Scholar 

  12. Kim, E., Lee, H.: New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE Trans. Fuzzy Syst. 8(5), 523–534 (2000)

    Article  Google Scholar 

  13. Gahinet, P., Nemirovski, A., Laub, A., Chilali, M.: LMI Control Toolbox. The Math Works Inc., Natick (1994)

    Book  Google Scholar 

  14. Johansson, M., Rantzer, A., Årzén, K.: Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Syst. 7(6), 713–722 (1999)

    Article  Google Scholar 

  15. Wang, L., Feng, G.: Piecewise \({\text{H}}_{\infty} \,\)controller design of discrete time fuzzy systems. IEEE Trans. Syst. Man Cybern. B 34(1), 682–686 (2004)

    Article  Google Scholar 

  16. Wang, W.J., Sun, C.H.: Relaxed stability and stabilization conditions for a T–S fuzzy discrete system. Fuzzy Set Syst. 156(2), 208–225 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang, W.J., Chen, Y.J., Sun, C.H.: Relaxed stabilization criteria for discrete-time T–S fuzzy systems based on switching fuzzy model and piecewise Lyapunov function. IEEE Trans. Syst. Man Cybern. B 37(3), 551–559 (2007)

    Article  MathSciNet  Google Scholar 

  18. Chung, H.Y., Wu, S.M., Chang, W.J.: Regional fuzzy control for nonlinear ship steering systems. Int. J. Innov. Comput. Inf. Control 4(7), 1635–1646 (2008)

    Google Scholar 

  19. Sun, C.H., Lin, S.W., Wang, Y.T.: Relaxed stabilization conditions for switching T–S fuzzy systems with practical constraints. Int. J. Innov. Comput. Inf. Control 8(6), 4133–4145 (2012)

    Google Scholar 

  20. Qiu, J., Feng, G., Gao, H.: Static-output-feedback control of continuous-time T–S fuzzy affine systems via piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 21(2), 245–261 (2013)

    Article  Google Scholar 

  21. Zhang, K., Jiang, B., Shi, P.: Fault estimation observer design for discrete-time Takagi-Sugeno fuzzy systems based on piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 20(1), 192–200 (2012)

    Article  Google Scholar 

  22. Xiang, W., Xiao, J., Han, L.: Switching PDC control for discrete-time T–S fuzzy system: a membership function ranking approach. J. Frankl. Inst. 351(7), 3536–3558 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tanaka, K., Iwasaki, M., Wang, H.O.: Switching control of an R/C hovercraft: stabilization and smooth switching. IEEE Trans. Syst. Man Cybern. Part B 31(6), 853–863 (2001)

    Article  Google Scholar 

  24. Chen, Y.J., Wang, W.J., Chang, C.L.: Guaranteed cost control for an overhead crane with practical constraints: fuzzy descriptor system approach. Eng. Appl. Artif. Intell. 22(4–5), 639–645 (2009)

    Article  Google Scholar 

  25. Du, H.P., Zhang, N.: Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint. IEEE Trans. Fuzzy Syst. 17(2), 343–356 (2009)

    Article  Google Scholar 

  26. Ariño, C., Pérez, E., Sala, A.: Guaranteed cost control analysis and iterative design for constrained Takagi-Sugeno systems. Eng. Appl. Artif. Intell. 23(8), 1420–1427 (2010)

    Article  Google Scholar 

  27. Chen, Y.J., Wang, W.J., Chang, C.L.: Guaranteed-cost fuzzy controller design for a self-sustaining bicycle with practical constraints. Asian J. Control 13(6), 831–844 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sun, C.H., Wang, Y.T., Chang, C.C.: Switching T–S fuzzy model-based guaranteed cost control for two-wheeled mobile robots. Int. J. Innov. Comput. Inf. Control 8(5(A)), 3015–3028 (2012)

    Google Scholar 

  29. Tanaka, M., Yamaguchi, K., Ogura, D., Chen, Y.J., Tanaka, K.: Nonlinear control of F16 aircraft via multiple nonlinear model generation for any trimmed equilibriums. Int. J. Fuzzy Syst. 16(2), 140–152 (2014)

    Google Scholar 

  30. Chang, W.J., Shih, Y.J.: Fuzzy control of multiplicative noised nonlinear systems subject to actuator saturation and \({\text{H}}_{\infty} \,\)performance constraints. Neurocomputing 148, 512–520 (2015)

    Article  Google Scholar 

  31. Saifia, D., Chadli, M., Karimi, H.R., Labiod, S.: Fuzzy control for electric power steering system with assist motor current input constraints. J. Frankl. Inst. 352(2), 562–576 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  32. Liu, X., Zhang, Q.: New approaches to \({\text{H}}_{\infty} \,\)controller designs based on fuzzy observers for T–S fuzzy systems via LMI. Automatica 39(9), 1571–1582 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  33. Tanaka, K., Ikeda, T., Wang, H.O.: Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, \({\text{H}}_{\infty} \,\)control theory, and linear matrix inequalities. IEEE Trans. Fuzzy Syst. 4(1), 1–13 (1996)

    Article  Google Scholar 

  34. Lee, K.R., Jeung, E.T., Park, H.B.: Robust fuzzy \({\text{H}}_{\infty} \,\)control for uncertain nonlinear systems via state feedback: an LMI approach. Fuzzy Set Syst. 120(1), 123–134 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  35. Tian, E., Yue, D., Yang, T.C., Gu, Z., Lu, G.: T–S fuzzy model-based robust stabilization for networked control systems with probabilistic sensor and actuator failure. IEEE Trans. Fuzzy Syst. 19(3), 553–561 (2011)

    Article  Google Scholar 

  36. Hu, S., Yue, D., Shi, M., Xie, X.: Discrete-time event-triggered control of nonlinear wireless networked control systems. Abstr. Appl. Anal. 2014, 14 (2014). doi:10.1155/2014/860438

    MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the Ministry of Science and Technology of Taiwan under the Grants MOST 103-2221-E-032-040, MOST 104-2221-E-032-028, and MOST 103-2632- E-001-MY3.

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  1. Department of Mechanical and Electro-mechanical Engineering, Tamkang University, Tamsui, 251, Taiwan

    Chung-Hsun Sun

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  1. Chung-Hsun Sun
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Correspondence to Chung-Hsun Sun.

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Sun, CH. Relaxed Stabilization Conditions for the T–S Fuzzy System with Input Constraints. Int. J. Fuzzy Syst. 18, 168–176 (2016). https://doi.org/10.1007/s40815-016-0153-5

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  • DOI: https://doi.org/10.1007/s40815-016-0153-5

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