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Admissibility Analysis for Nonlinear Singular System with Time-Delay Via T–S Fuzzy Model

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Abstract

This paper is concerned with the problem of admissibility analysis of Takagi–Sugeno fuzzy singular systems with time-varying delay. The time-delay is assumed to be available online and interval-like type. Based on delay partitioning technique and the free-weighting-matrix approach combined with the constructed Lyapunov–Krasovskii functional, a sufficient condition is obtained such that the system is regular, impulse free, and asymptotically stable. All obtained conditions are dependent on time-delay and partitioning number. These conditions are formulated in the form of linear matrix inequalities. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed theories.

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References

  1. Ahn, C.K.: Passive and exponential filter design for fuzzy neural networks. Inf. Sci. 238(30), 126–137 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ahn, C.K.: T–S fuzzy \({H}_{\infty }\) synchronization for chaotic systems via delayed output feedback control. Nonlinear Dyn. 59(4), 535–543 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahn, C.K.: Some new results on stability of Takagi–Sugeno fuzzy Hopfield neural networks. Fuzzy Sets Syst. 179(1), 100–111 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baser, U., Sahin, U.: Improved delay-dependent robust stabilization of singular systems. Int. J. Innov. Comput. Inf. Control 7(1), 177–187 (2011)

    Google Scholar 

  5. Benzaouia, A., Hajjaji, A.E.: Delay-dependent stabilization conditions of controlled positive T–S fuzzy systems with time varying delay. Int. J. Innov. Comput. Inf. Control 7(4), 1533–1547 (2011)

    Google Scholar 

  6. Chang, W.-J., Tsai, Y.-S., Ku, C.-C.: Fuzzy fault tolerant control via Takagi–Sugeno fuzzy models for nonlinear systems with multiplicative noises. Int. J. Fuzzy Syst. 16(3), 338–349 (2014)

    MathSciNet  Google Scholar 

  7. Dai, L.: Singular Control Systems. Springer, Berlin (1989)

    Book  MATH  Google Scholar 

  8. Er, M.J., Liu, F., Li, M.B.: Self-constructing fuzzy neural networks with extended Kalman filter. Int. J. Fuzzy Syst. 12(1), 66–72 (2010)

    Google Scholar 

  9. Gassara, H., Kchaou, M., El Hajjaji, A., Chaabane, M.: Control of time delay fuzzy descriptor systems with actuator saturation. Circuits Syst. Signal Process. 33, 3739–3756 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gassaraa, H., ElHajjajia, A., Kchaoub, M., Chaabaneb, M.: Observer based (Q, V, R)-dissipative controlfor T–S fuzzy descriptor systems with time delay. J. Frankl. Inst. 351, 187–206 (2014)

    Article  Google Scholar 

  11. Huang, C.: Stability analysis of discrete singular fuzzy systems. Fuzzy Sets Syst. 151, 155–165 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Huang, C.: Stability analysis and controller synthesis for fuzzy descriptor systems. Int. J. Syst. Sci. 44(1), 23–33 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jong, H.: Delay-dependent robust \({H}_{\infty }\) control for discrete-time uncertain singular systems with interval time-varying delays in state and control input. J. Frankl. Inst. 347(9), 1704–1722 (2014)

    MathSciNet  MATH  Google Scholar 

  14. Kchaouli, 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 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. 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 

  16. Lee, C.-H., Cheng, H.-T.: Identification and fuzzy controller design for nonlinear uncertain systems with input time-delay. Int. J. Fuzzy Syst. 11(2), 73–86 (2009)

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, H., Yin, S., Pan, Y., Lam, H.K.: Model reduction for interval type-2 Takagi–Sugeno fuzzy systems. Automatica 61, 308–314 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Li, H., Gao, Y.: Peng Shi, and X. Zhao. Output-feedback control for T–S fuzzy delta operator systems with time-varying delays via an input-output approach. IEEE Trans. Fuzzy Syst. 23(4), 1100–1112 (2015)

    Article  Google Scholar 

  20. Li, X., Rakkiyappan, R., Balasubramaniam, P.: Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J. Frankl. Inst. 348(2), 135–155 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, L., Zhang, Q., Zhu, B.: Fuzzy stochastic optimal guaranteed cost control of bio-economic singular Markovian jump systems. IEEE Trans. Cybern. (2015). doi: 10.1109/TCYB.2014.2375957

    Google Scholar 

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

    Article  Google Scholar 

  23. Liu, L., Peng, J., Wu, B.: \({H}_{\infty }\) control of singular time-delay systems via discretized Lyapunov functional. J. Frankl. Inst. 348(4), 749–762 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Su, X., Wu, L., Shi, P., Philip Chen, C.L.: Model approximation for fuzzy switched systems with stochastic perturbation. IEEE Trans. Fuzzy Syst. 23(5), 1458–1473 (2015)

    Article  Google Scholar 

  25. Su, X., Wu, L., Shi, P., Song, Y.-D.: A novel approach to output feedback control of fuzzy stochastic systems. Automatica 50(12), 3268–3275 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Taniguchi, T., Tanaka, K., Wang, H.: Fuzzy descriptor systems and nonlinear model following control. IEEE Trans. Fuzzy Syst. 8, 442–452 (2000)

    Article  Google Scholar 

  27. Xie, X., Yue, D., Ma, T., Zhu, X.: Further studies on control synthesis of discrete-time T–S fuzzy systems via augmented multi-indexed matrix approach. IEEE Trans. Cybern. 44(12), 2784–2791 (2014)

    Article  Google Scholar 

  28. X. Xie, D. Yue, H. Zhang, and Y. Xue. Control synthesis of discrete-time T–S fuzzy systems via a multi-instant homogenous polynomial approach, IEEE Trans. Cybern. (2015). doi:10.1109/TCYB.2015.2411336

    Google Scholar 

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

    MATH  Google Scholar 

  30. 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  MATH  Google Scholar 

  31. Yang, Z., Yang, Y.: New delay-dependent stability analysis and synthesis of T–S fuzzy systems with time-varying delay. Int. J. Robust Nonlinear 20, 313–322 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  32. Yoneyama, J., Ichikawa, A.: \({H}_{\infty }\) control for Takagi–Sugeno fuzzy descriptor systems. IEEE Conf. Syst. Man Cybern. 3, 28–33 (1999)

    Google Scholar 

  33. Zhang, H., Shen, 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 

  34. Zhang, H., Xie, X.: Relaxed stability conditions for continuous-time T–S fuzzy-control systems via augmented multi-indexed matrix approach. IEEE Trans. Fuzzy Syst. 19(3), 478–492 (2011)

    Article  Google Scholar 

  35. Zhang, H., Zhang, J., Yang, G.-H., Luo, Y.: Leader-based optimal coordination control for the consensus problem of multi-agent differential games via fuzzy adaptive dynamic programming. IEEE Trans. Fuzzy Syst. 23(1), 152–163 (2015)

    Article  Google Scholar 

  36. Zhang, L., Tong, S., Li, Y.: Adaptive fuzzy output-feedback control with prescribed performance for uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 16(2), 212–221 (2014)

    Article  MathSciNet  Google Scholar 

  37. Zhou, S., Zheng, W.: Robust \({H}_{\infty }\) control of delayed singular systems with linear fractional parametric uncertainties. J. Frankl. Inst. 346(2), 147–158 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. Yue, D., Tian, E., Zhang, Y., Peng, C.: Delay-distribution-dependent stability and stabilization of T–S fuzzy systems with probabilistic interval delay. IEEE Trans. Syst. Man Cybern. Part B-Cybern. 39(2), 503–516 (2009)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported in part by the National Natural Science Foundation of China under Grant No. 61463001, the Natural Science Foundation of Heilongjiang Province of China under Grant Nos. F201331 and F201440, Project funded by Heilongjiang Province Postdoctoral Science Foundation under Grant No. LBH-Z15043.

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Authors and Affiliations

  1. School of Computer and Control Engineering, Qiqihar University, Qiqihar, 161002, People’s Republic of China

    Chunsong Han & Honglie Zhang

  2. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Yi Zeng

  3. College of Automation, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Yuxin Zhao

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  1. Chunsong Han
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  2. Yi Zeng
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  3. Honglie Zhang
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  4. Yuxin Zhao
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Correspondence to Yuxin Zhao.

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Han, C., Zeng, Y., Zhang, H. et al. Admissibility Analysis for Nonlinear Singular System with Time-Delay Via T–S Fuzzy Model. Int. J. Fuzzy Syst. 19, 207–214 (2017). https://doi.org/10.1007/s40815-015-0138-9

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  • DOI: https://doi.org/10.1007/s40815-015-0138-9

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