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Admissibility and Admissibilization of Singular Polynomial Fuzzy Systems with Time-Varying Delay

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Abstract

This paper addresses the admissibility analysis and the polynomial fuzzy controller design for a class of singular polynomial fuzzy systems with time-varying delay. Firstly, according to Lyapunov stability theory, a sufficient condition is obtained by means of sum-of-squares (SOS) to ensure that the closed-loop singular polynomial fuzzy system is admissible. Secondly, by the help of the two equivalent sets, SOS-based admissibility conditions are proposed to avoid solving the equality conditions and the polynomial fuzzy controller is designed. Finally, three examples validate the usefulness and superiority of the proposed design procedure compared with existing results.

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References

  1. Liu, P., Zhang, Q., Yang, X., Yang, L.: Passivity and optimal control of descriptor biological complex systems. IEEE Trans. Autom. Control 53, 122–125 (2008)

    Article  MathSciNet  Google Scholar 

  2. Duan, G.R.: Analysis and design of descriptor linear systems. Springer, New York (2010)

    Book  Google Scholar 

  3. Li, L., Zhang, Q., Zhu, B.: Fuzzy stochastic optimal guaranteed cost control of bio-economic singular markovian jump systems. IEEE Trans. Cybern. 45(11), 2512–2521 (2015)

    Article  Google Scholar 

  4. Feng, Z., Lam, J., Gao, H.: α-dissipativity analysis of singular time-delay systems. Automatica 47(11), 2548–2552 (2011)

    Article  MathSciNet  Google Scholar 

  5. Feng, Z., Lam, J.: On reachable set estimation of singular systems. Automatica 52, 146–153 (2015)

    Article  MathSciNet  Google Scholar 

  6. Zheng, M., Yang, S., Li, L.: Sliding mode control for fuzzy Markovian jump singular system with time-varying delay. Int. J. Control, Autom. Syst 17(7), 1677–1686 (2019)

    Article  Google Scholar 

  7. Li, W., Feng, Z., Sun, W., Zhang, J.: Admissibility analysis for Takagi-Sugeno fuzzy singular systems with time-delay. Neurocomputing 205, 336–340 (2016)

    Article  Google Scholar 

  8. Lian, Z., He, Y., Zhang, C.-K., Wu, M.: Stability and stabilization of T-S fuzzy systems with time-varying delays via delay-product-type functional method. IEEE Trans. Cybern. 50(6), 2580–2589 (2019)

    Article  Google Scholar 

  9. Datta, R., Dey, R., Bhattacharya, B., Saravanakumar, R., Kwon, O.-M.: Stability and stabilization of T-S fuzzy systems with variable delays via new bessel-legendre polynomial based relaxed integral inequality. Inform. Sciences 522, 99–123 (2020)

    Article  MathSciNet  Google Scholar 

  10. Xu, S., Song, B., Lu, J., Lam, J.: Robust stability of uncertain discrete-time singular fuzzy systems. Fuzzy Sets Syst. 158(20), 2306–2316 (2007)

    Article  MathSciNet  Google Scholar 

  11. Xing, S., Zhang, Q., Zhu, B.: Mean-square admissibility for stochastic T-S fuzzy singular systems based on extended quadratic lyapunov function approach. Fuzzy Sets Syst. 307, 99–114 (2017)

    Article  MathSciNet  Google Scholar 

  12. Sun, W., Su, S.-F., Wu, Y., Xia, J., Nguyen, V.-T.: Adaptive fuzzy control with high-order barrier lyapunov functions for high-order uncertain nonlinear systems with full-state constraints. IEEE Trans. Cybern. 50(8), 3424–3432 (2000)

    Article  Google Scholar 

  13. Lin, C., Wang, Q.G., Lee, T.H.: Stability and stabilization of a class of fuzzy time-delay descriptor systems. IEEE Trans. Fuzzy Syst. 14(4), 542–551 (2006)

    Article  Google Scholar 

  14. Wang, H., Zhou, B., Lu, R., Xue, A.: New stability and stabilization criteria for a class of fuzzy singular systems with time-varying delay. J. Franklin Inst. 351(7), 3766–3781 (2014)

    Article  MathSciNet  Google Scholar 

  15. Sun, C., Wang, F., He, X.: Delay-dependent stability and stabilization criteria for T-S fuzzy singular systems with interval time-varying delay by improved delay partitioning approach. SpringerPlus 5(1), 349 (2016)

    Article  Google Scholar 

  16. Han, C., Zeng, Y., Zhang, H., Zhao, Y.: Admissibility analysis for nonlinear singular system with time-delay via T-S fuzzy model. Int. J. Fuzzy Syst. 19(1), 207–214 (2016)

    Article  MathSciNet  Google Scholar 

  17. Qiao, L., Zhang, Q., Zhang, G.: Admissibility analysis and control synthesis for T-S fuzzy descriptor systems. IEEE Trans. Fuzzy Syst. 25(4), 729–740 (2016)

    Article  MathSciNet  Google Scholar 

  18. Zhang, X., Zhao, Z.: Normalization and stabilization for rectangular singular fractional order T-S fuzzy systems. Fuzzy Sets Syst. 381, 140–153 (2020)

    Article  MathSciNet  Google Scholar 

  19. Feng, Z., Shi, P.: Admissibilization of singular interval-valued fuzzy systems. IEEE Trans. Fuzzy Syst. 25(6), 1765–1776 (2016)

    Article  Google Scholar 

  20. Feng, Z., Zhang, H., Du, H., Jiang, Z.: Admissibilisation of singular interval type-2 Takagi-Sugeno fuzzy systems with time delay. IET Control Theory Appl. 14(8), 1022–1032 (2020)

    Article  Google Scholar 

  21. Tanaka, K., Yoshida, H., Ohtake, H., Wang, H.: A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems. IEEE Trans. Fuzzy Syst. 17(4), 911–922 (2009)

    Article  Google Scholar 

  22. Narimani, M., Lam, H.-K.: SOS-based stability analysis of polynomial fuzzy-model-based control systems via polynomial membership functions. IEEE Trans. Fuzzy Syst. 18(5), 862–871 (2010)

    Article  Google Scholar 

  23. Liu, C., Lam, H.K.: Design of a polynomial fuzzy observer controller with sampled-output measurements for nonlinear systems considering unmeasurable premise variables. IEEE Trans. Fuzzy Syst. 23(6), 2067–2079 (2015)

    Article  Google Scholar 

  24. Xiao, B., Lam, H.-K., Li, H.: Stabilization of interval type-2 polynomial-fuzzy-model-based control systems. IEEE Trans. Fuzzy Syst. 25(1), 205–217 (2016)

    Article  Google Scholar 

  25. Zhao, Y., He, Y., Feng, Z., Shi, P., Du, X.: Relaxed sum-of-squares based stabilization conditions for polynomial fuzzy-model-based control systems. IEEE Trans. Fuzzy Syst. 27(9), 1767–1778 (2018)

    Article  Google Scholar 

  26. Ye, D., Li, X.: State feedback controller design for general polynomial-fuzzy-model-based systems with time-varying delay. Int. J. Fuzzy Syst. 21(2), 583–591 (2019)

    Article  MathSciNet  Google Scholar 

  27. Pang, B., Zhang, Q.: Sliding mode control for polynomial fuzzy singular systems with time delay. IET Control Theory Appl. 12(10), 1483–1490 (2018)

    Article  MathSciNet  Google Scholar 

  28. Gao, R., Zhang, Q., Li, J.: Integral sliding mode control for polynomial fuzzy descriptor systems, in: In Proceeding of the 37th Chinese Control Conference, Hubei Wuhan, 2018, pp. 3329–3334 (2018)

  29. Pang, B., Zhang, Q.: Interval observers design for polynomial fuzzy singular systems by utilizing sum-of-squares program. IEEETrans. Syst., Man, Cybern.: Syst. 50(6), 1999–2006 (2018)

    Google Scholar 

  30. Xu, S., Lam, J.: Robust Control and Filtering of Singular Systems. Springer, Berlin (2006)

    MATH  Google Scholar 

  31. Xie, L.: Output feedback α control of systems with parameter uncertainty. Int. J. control 63(4), 741–750 (1996)

    Article  MathSciNet  Google Scholar 

  32. Xia, Y., Boukas, E.-K., Shi, P., Zhang, J.: Stability and stabilization of continuous-time singular hybrid systems. Automatica 45(6), 1504–1509 (2009)

    Article  MathSciNet  Google Scholar 

  33. Feng, Z., Shi, P.: Two equivalent sets: Application to singular systems. Automatica 77, 198–205 (2017)

    Article  MathSciNet  Google Scholar 

  34. Chen, B., Liu, X.: Delay-dependent robust \(H_\infty\) control for T-S fuzzy systems with time delay. IEEE Trans. Fuzzy Syst. 13(4), 544–556 (2005)

    Article  Google Scholar 

  35. Tanaka, K., Wang, H.O.: Fuzzy control systems design and analysis: a linear matrix inequality approach. Wiley, Amsterdam (2004)

    Google Scholar 

  36. Li, J., Zhang, Q., Yan, X.-G., Spurgeon, S.K.: Observer-based fuzzy integral sliding mode control for nonlinear descriptor systems. IEEE Trans. Fuzzy Syst. 26(5), 2818–2832 (2018)

    Article  Google Scholar 

  37. Lam, H.-K., Leung, F.H., Tam, P.K.-S.: Stable and robust fuzzy control for uncertain nonlinear systems. IEEE Transa. Syst. Man Cybern. Part A Syst. Humans 30(6), 825–840 (2000)

    Article  Google Scholar 

  38. Sun, W., Su, S.-F., Wu, Y., Xia, J.: A novel adaptive fuzzy control for output constrained stochastic non-strict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2969909

    Article  Google Scholar 

  39. Sun, K., Jianbin, Q., Karimi, H.R., Fu, Y.: Event-triggered robust fuzzy adaptive finite-time control of nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2979129

    Article  Google Scholar 

  40. Sun, K., Qiu, J., Karimi, H.R., Gao, H.: A novel finite-time control for nonstrict feedback saturated nonlinear systems with tracking error constraint, IEEE Trans. Syst., Man, Cybern., Syst. (2019). https://doi.org/10.1109/TSMC.2019.2958072

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 62073094, in part by the Natural Science Foundation of Heilongjiang Province of China under Grant YQ2019F004, in part by the Fundamental Research Funds for the Central Universities under Grant 3072020CFJ0409, in part by the Fundamental Research Funds for the Provincial Universities under Grant 2019J00046, in part by the China Postdoctoral Science Foundation under Grant 2018M63034 and Grant 2018T110275.

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Authors and Affiliations

  1. College of Automation, Harbin Engineering University, Harbin, 150001, China

    Zhiguang Feng, Yang Yang, Yuxin Zhao & Xin Yuan

  2. School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, 2522, NSW, Australia

    Zhiguang Feng & Zhengyi Jiang

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  1. Zhiguang Feng
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  2. Yang Yang
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Correspondence to Yang Yang.

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Feng, Z., Yang, Y., Jiang, Z. et al. Admissibility and Admissibilization of Singular Polynomial Fuzzy Systems with Time-Varying Delay. Int. J. Fuzzy Syst. 23, 81–93 (2021). https://doi.org/10.1007/s40815-020-00965-z

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  • DOI: https://doi.org/10.1007/s40815-020-00965-z

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