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Robust \(H_\infty\) Observer-Based Control for a Class of (TS) Fuzzy Descriptor Systems with Time-Varying Delay

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Abstract

In this study, a robust output feedback \(H_\infty\) learning control strategy for a class of Takagi–Sugeno (TS) fuzzy descriptor systems with time-varying delay and external disturbance is developed. The system is subject to uncertainties and unmeasurable state variables. The appealing attributes of this approach include (i) an appropriate Lyapunov–Krasovskii functional to derive a delay-dependent sufficient condition to guarantee that the system is robustly admissible with \(H_\infty\) performance and (ii) the design of an observer-based controller such that the closed-loop system exhibits the admissibility as well as the \(H_\infty\) performance requirement with robustness against uncertainties and time delay. Finally, the validity and applicability of the proposed approach are illuminated by examples.

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References

  1. Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences, vol. 118. Springer, New York (1989)

  2. Gassara, H., Hajjaji, A.E., Kchaou, M., Chaabane, M.: Robust H\(_\infty\) reliable control of time delay nonlinear systems via takagi–sugeno fuzzy models. Int. J. Syst. Sci. 45(3), 667–681 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kchaou, M., Toumi, A., Souissi, M.: Robust reliable guaranteed cost piecewise fuzzy control for discrete-time nonlinear systems with time-varying delay and actuator failures. Int. J. Gen. Syst. 40(5), 531–558 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mahmoud, M.: Switched Time-Delay Systems. Springer, Boston (2010)

    Book  MATH  Google Scholar 

  5. Xia, Y., Fu, M., Shi, P.: Analysis and Synthesis of Dynamical Systems with Time-Delays. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  6. Duan, G.: Analysis and Design of Descriptor Linear Systems. Springer, New York (2010)

    Book  MATH  Google Scholar 

  7. Kchaou, M., Gassara, H., El-Hajjaji, A.: Robust observer-based control design for uncertain singular systems with time-delay. Int. J. Adapt. Control Signal Process 28(2), 169–183 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ma, S., Cheng, Z., Zhang, C.: Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays. IET Control Theory Appl. 1(4), 1086–1095 (2007)

    Article  MathSciNet  Google Scholar 

  9. Yang, F., Zhang, Q.: Delay-dependent \(H_\infty\) control for linear descriptor systems with delay in state. J. Control Theory Appl. 3(1), 76–84 (2005)

    Article  MathSciNet  Google Scholar 

  10. Zhang, H., Shenb, Y., Feng, G.: Delay-dependent stability and \(H_\infty\) control for a class of fuzzy descriptor systems with time-delay. Fuzzy Sets Syst. 160, 1689–1707 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhou, S., Lam, J.: Robust stabilization of delayed singular systems with linear fractional parametric uncertainties. Circuits Syst. Signal Process 22(6), 579–588 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Boukas, E.: Singular linear systems with delay : \(H_{\infty }\) stabilization. Optim. Control Appl. Methods 28, 259–274 (2007)

    Article  MathSciNet  Google Scholar 

  13. Feng, J., Cui, P., Cheng, Z.: \(H_\infty\) output feedback control for descriptor systems with delayed states. J. Control Theory Appl. 4, 341–347 (2005)

    MATH  Google Scholar 

  14. Kchaou, M., Tadeo, F., Chaabane, M.: A partitioning approach for H\(_\infty\) control of singular time-delay systems. Optim. Control Appl. Methods 34(4), 472–486 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modelling and control. Trans. Syst. Man Cybern. 15, 116–132 (1985)

    Article  MATH  Google Scholar 

  16. Benzaouia, A., Oubah, R.: Stability and stabilization by output feedback control of positive Takagi–Sugeno fuzzy discrete-time systems with multiple delays. Nonlinear Anal. 11, 154–170 (2014)

    MathSciNet  MATH  Google Scholar 

  17. Chen, B., Lin, C., Liu, X., Tong, S.: Guaranteed cost control of TS fuzzy systems with input delay. Int. J. Robust Nonlinear Control 18, 1230–1256 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kchaou, M., Toumi, A., Souissi, M.: Delay-dependent \(H_\infty\) resilient output fuzzy control for nonlinear discrete-time systems with time-delay. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 19(2), 229–250 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kchaoua, M., Souissi, M., Toumi, A.: Robust reliable guaranteed cost piecewise fuzzy control for discrete-time nonlinear systems with time-varying delay and actuator failures. Int. J. Gener. Syst. 40(5), 531–558 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Klug, M., Castelan, E., Leite, V., Silva, L.F.: Fuzzy dynamic output feedback control through nonlinear Takagi–Sugeno models. Fuzzy Sets Syst. 263(15), 92–111 (2015)

    Article  MathSciNet  Google Scholar 

  21. Wu, H.: Delay-dependent \(H_\infty\) fuzzy observer-based control for discrete-time nonlinear systems with state delay. Fuzzy Sets Syst. 159, 2696–2712 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhang, B., Xu, S.: Delay-dependent robust \(H_\infty\) control for uncertain discrete-time fuzzy systems with time-varying delays. IEEE Trans. Fuzzy Syst. 17(4), 809–823 (2009)

    Article  Google Scholar 

  23. Kchaou, M., Souissi, M., Toumi, A.: Delay-dependent stability and robust \(L_2 -L_\infty\) control for a class of fuzzy descriptor systems with time-varying delay. Int. J. Robust Nonlinear Control 23(3), 284–304 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Li, X., Rakkiyappan, R.: Stability results for takagi–sugeno fuzzy uncertain bam neural networks with time delays in the leakage term. Neural Comput. Appl. 22(1), 203–219 (2013)

    Google Scholar 

  25. Lin, C., Wang, Q., Lee, T.: Stability and stabilization of a class of fuzzy time-delay descriptor systems. IEEE Trans. Fuzzy Syst. 14, 542–551 (2006)

    Article  Google Scholar 

  26. Rakkiyappan, R., Chandrasekar, A., Lakshmanan, S.: Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays. Int. J. Syst. Sci. (2014). doi:10.1080/00207721.2014.981236

  27. Su, X., Zheng, W., Zhang, N.: Optimal control for TS fuzzy descriptor systems with time domain hard constraints. Int. J. Inf. Syst. Sci 5(3–4), 447–456 (2009)

    MathSciNet  Google Scholar 

  28. Tian, W., Zhang, H.: Optimal guaranteed cost control for fuzzy descriptor systems with time-varying delay. J. Syst. Eng. Electron 19, 584–591 (2008)

    Article  MATH  Google Scholar 

  29. Qin, L., Qingling, Z., Yanjuan, Z., Yichun, A.: Observer-based passive control for descriptor systems with time-delay. J. Syst. Eng. Electron. 20(1), 120–128 (2009)

    Google Scholar 

  30. Zhang, Y., Cheng, W., Mu, X., Guo, X.: Observer-based finite-time \(H_\infty\) control of singular Markovian jump systems. J. Appl. Math. (2012). doi:10.1155/2012/205727

  31. Gassara, H., Hajjaji, A.E., Kchaou, M., Chaabane, M.: Observer based (\(Q, V, R)-\alpha\) -dissipative control for TS fuzzy descriptor systems with time delay. J. Frankl. Inst. 351(1), 187–206 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  32. Fan, H., Meng, M., e Feng, J.: Observers of fuzzy descriptor systems with time-delays. Abstract and Applied Analysis (714518), 1–9 (2014)

  33. Xu, S., Dooren, P.V., Stefan, R., Lam, J.: Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. Autom. Control 47(7), 1122–1128 (2002)

    Article  MathSciNet  Google Scholar 

  34. Fridman, E.: Stability of linear descriptor systems with delay : a Lyapunov-based approach. J. Math. Anal. Appl. 273, 24–44 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  35. Peterson, I.: A stabilization algorithm for a class uncertain linear systems. Syst. Control Lett. 8(4), 351–357 (1987)

    Article  MathSciNet  Google Scholar 

  36. Gu, K., Kharitonov, V., Chen, J.: Stability of Time-Delay Systems. Springer, Berlin (2003)

    Book  MATH  Google Scholar 

  37. Yu, J., Tan, J., Jiang, H., Liu, H.: Dynamic output feedback control for markovian jump systems with time-varying delays. IET Control Theory Appl. 6(6), 803–812 (2012)

    Article  MathSciNet  Google Scholar 

  38. M Kchaou, Souissi, M., Toumi, A.: Delay-dependent stability and robust \(L_2 -L_\infty\) control for a class of fuzzy descriptor systems with time-varying delay. Int. J. Robust Nonlinear Control 2011. doi:10.1002/rnc.1832

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Authors and Affiliations

  1. Electrical Department, College of Engineering, University of Hail, 2440, Hail, Kingdom of Saudi Arabia

    Mourad Kchaou

  2. Laboratory of Sciences and Techniques of Automatic control & computer engineering (Lab-STA), University of Sfax, P. O. Box 1173, 3038, Sfax, Tunisia

    Mourad Kchaou

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  1. Mourad Kchaou
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Correspondence to Mourad Kchaou.

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Kchaou, M. Robust \(H_\infty\) Observer-Based Control for a Class of (TS) Fuzzy Descriptor Systems with Time-Varying Delay. Int. J. Fuzzy Syst. 19, 909–924 (2017). https://doi.org/10.1007/s40815-016-0200-2

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  • DOI: https://doi.org/10.1007/s40815-016-0200-2

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