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Fuzzy model-based nonfragile control of switched discrete-time systems

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Abstract

This paper is concerned with the problem of nonfragile control for a class of fuzzy switched systems with mode-dependent time-varying delays. By constructing novelty Lyapunov function and employing a novel extended reciprocally convex discrete-time inequality, new sets of delay-variation-dependent stability criteria are derived. A nonfragile fuzzy controller is developed, via the parallel distributed compensation technique and stochastic analysis method. At last, numerical simulation is provided to show the effectiveness of achieved result.

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References

  1. Shen, H., Wang, T., Chen, M., Lu, J.: Nonfragile mixed \(\cal{H}_{\infty }/\cal{L}_{1}-\cal{L}_{\infty }\) state estimation for repeated scalar nonlinear systems with Markov jumping parameters and redundant channels. Nonlinear Dyn. (2018). https://doi.org/10.1007/s11071-017-3899-x

    Google Scholar 

  2. He, S., Xu, H.: Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach. Nonlinear Dyn. 80(3), 1159–1171 (2015)

    Article  MATH  Google Scholar 

  3. Zhang, D., Shi, P., Zhang, W., Yu, L.: Energy-efficient distributed filtering in sensor networks: a unified switched system approach. IEEE Trans. Cybern. 47(7), 1618–1629 (2017)

    Google Scholar 

  4. Tian, E., Yue, D., Yang, T.: Analysis and synthesis of randomly switched systems with known sojourn probabilities. Inf. Sci. 277, 481–491 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Tian, E., Wong, W.K., Yue, D.: Robust \({\cal{H}}_{\infty }\) control for switched systems with input delays: a sojourn-probability-dependent method. Inf. Sci. 283, 22–35 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. He, S., Song, J., Liu, F.: Robust finite-time bounded controller design of time-delay conic nonlinear systems using sliding mode control strategy. IEEE Trans. Syst. Man Cybern. Syst. (2017). https://doi.org/10.1109/TSMC.2017.2695483

    Google Scholar 

  7. Meng, X., Zhao, S., Feng, T., Zhang, T.: Dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis. J. Math. Anal. Appl. 433(1), 227–242 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wu, Z., Cui, M., Shi, P., Karimi, H.R.: Stability of stochastic nonlinear systems with state-dependent switching. IEEE Trans. Autom. Control 58(8), 1904–1918 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, F., Meng, X., Cui, Y.: Nonlinear stochastic analysis for a stochastic SIS epidemic model. J. Nonlinear Sci. Appl. 10(9), 5116–5124 (2017)

    Article  MathSciNet  Google Scholar 

  10. Meng, X., Chen, L., Wang, X.: Some new results for a logistic almost periodic system with infinite delay and discrete delay. Nonlinear Anal. Real World Appl. 10(3), 1255–1264 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, B., Yan, J., Cheng, J., Zhong, S.: New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals. Appl. Math. Comput. 314, 322–333 (2017)

    MathSciNet  Google Scholar 

  12. Zhang, L., Zhuang, S., Shi, P., Zhu, Y.: Uniform tube based stabilization of switched linear systems with mode-dependent persistent dwell-time. IEEE Trans. Autom. Control 60(11), 2994–2999 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang, S., Meng, X., Zhang, T.: Dynamics analysis and numerical simulations of a stochastic non-autonomous predator-prey system with impulsive effects. Nonlinear Anal. Hybrid Syst. 26, 19–37 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, Y., Xia, Y., Li, H., Zhou, P.: A new integral sliding model design method for nonlinear stochastic systems. Automatica 90C, 304–309 (2018)

    Article  MATH  Google Scholar 

  15. Wang, Y., Xia, Y., Shen, H., Zhou, P.: SMC design for robust stabilization of nonlinear Markovian jump singular systems. IEEE Trans. Autom. Control 63(1), 219–224 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  16. Su, X., Shi, P., Wu, L., Song, Y.D.: Fault detection filtering for nonlinear switched stochastic systems. IEEE Trans. Autom. Control 61(5), 1310–1315 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Cheng, J., Park, J.H., Zhang, L., Zhu, Y.: An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies. IEEE Trans. Fuzzy Syst. 26(1), 6–18 (2018)

    Article  Google Scholar 

  18. Park, M.J., Kwon, O.M.: Stability and stabilization of discrete-time T–S fuzzy systems with time-varying delay via Cauchy–Schwartz-based summation inequality. IEEE Trans. Fuzzy Syst. 25(1), 128–140 (2017)

    Article  Google Scholar 

  19. Park, M.J., Kwon, O.M., Choi, S.G.: Stability analysis of discrete-time switched systems with time-varying delays via a new summation inequality. Nonlinear Anal. Hybrid Syst. 23, 76–90 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kwon, O.M., Park, M.J., Lee, S.H., Park, J.H., Lee, S.M.: Stability and stabilization of T–S fuzzy systems with time-varying delays via augmented Lyapunov–Krasovskii functionals. Inf. Sci. 372, 1–15 (2016)

    Article  MathSciNet  Google Scholar 

  21. Meng, X., Wang, L., Zhang, T.: Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment. J. Appl. Anal. Comput. 6(3), 865–875 (2016)

    MathSciNet  Google Scholar 

  22. Wang, B., Cheng, J., Zhan, J.: A sojourn probability approach to fuzzy-model-based reliable control for switched systems with mode-dependent time-varying delays. Nonlinear Anal. Hybrid Syst. 26, 239–253 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  23. Banu, L.J., Balasubramaniam, P.: Robust stability and stabilization analysis for discrete-time randomly switched fuzzy systems with known sojourn probabilities. Nonlinear Analysis Hybrid Syst. 17, 128–143 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Seuret, A., Gouaisbaut, F., Fridman, E.: Stability of discrete-time systems with time-varying delays via a novel summation inequality. IEEE Trans. Autom. Control 60(10), 2740–2745 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang, B., Zhong, S., Dong, X.: On the novel chaotic secure communication scheme design. Commun. Nonlinear Sci. Numer. Simul. 39, 108–117 (2016)

    Article  MathSciNet  Google Scholar 

  26. Zhang, T., Ma, W., Meng, X., Zhang, T.: Periodic solution of a prey–predator model with nonlinear state feedback control. Appl. Math. Comput. 266, 95–107 (2015)

    MathSciNet  Google Scholar 

  27. Wu, L., Yang, X., Lam, H.K.: Dissipativity analysis and synthesis for discrete-time T–S fuzzy stochastic systems with time-varying delay. IEEE Trans. Fuzzy Syst. 22(2), 380–394 (2014)

    Article  Google Scholar 

  28. Xie, X., Yue, D., Zhang, H., Peng, C.: Control synthesis of discrete-time T-S fuzzy systems: reducing the conservatism whilst alleviating the computational burden. IEEE Trans. Cybern. (2016). https://doi.org/10.1109/TCYB.2016.2582747

    Google Scholar 

  29. Luo, J., Zhao, J.: A generalized multiple Lyapunov functions method based non-fragile guaranteed cost control for uncertain switched fuzzy systems. Appl. Math. Comput. 237, 494–500 (2014)

    MathSciNet  MATH  Google Scholar 

  30. Park, M.J., Kwon, O.M., Park, J.H., Lee, S.M., Cha, E.J.: Synchronization of discrete-time complex dynamical networks with interval time-varying delays via non-fragile controller with randomly occurring perturbation. J. Frankl. Inst. 351, 4850–4871 (2014)

    Article  MathSciNet  Google Scholar 

  31. Wu, Z.G., Park, J.H., Su, H., Chu, J.: Non-fragile synchronization control for complex networks with missing data. Int. J. Control 86, 555–566 (2013)

    Article  MATH  Google Scholar 

  32. Wu, Z.G., Dong, S., Shi, P., Su, H., Huang, T., Lu, R.: Fuzzy-model-based nonfragile guaranteed cost control of nonlinear Markov jump systems. IEEE Trans. Syst. Man Cybern. (2017). https://doi.org/10.1109/TSMC.2017.2675943

    Google Scholar 

  33. Sakthivel, R., Aravindh, D., Selvaraj, P., Vimal, S., Kumar, S., Anthoni, M.: Vibration control of structural systems via robust non-fragile sampled-data control scheme. J. Frankl. Inst. 3, 1265–1284 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  34. Zhang, C., He, Y., Jiang, L., Wang, Q., Wu, M.: Stability analysis of discrete-time neural networks with time-varying delay via an extended reciprocally convex matrix inequality. IEEE Trans. Cybern. (2017). https://doi.org/10.1109/TCYB.2017.2665683

    MATH  Google Scholar 

  35. Khargonekar, P.P., Petersen, I.R., Zhou, K.: Robust stabilization of uncertain linear systems: quadratic stabilizability and \({\cal{H}}_{\infty }\) control theory. IEEE Trans. Autom. Control 35(3), 356–361 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  36. Park, P., Ko, J.W.: Stability and robust stability for systems with a time-varying delay. Automatica 43(10), 1855–1858 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  37. Sakthivel, R., Saravanakumar, T., Ma, Y., Anthoni, S.M.: Finite-time resilient reliable sampled-data control for fuzzy systems with randomly occurring uncertainties. Fuzzy Sets Syst. 329, 1–18 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  38. Ghaoui, L.E., Oustry, F., AitRami, M.: A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Auto. Control 42, 1171–1176 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang, L., Ning, Z., Shi, P.: Input-output approach to control for fuzzy Markov jump systems with time-varying delays and uncertain packet dropout rate. IEEE Trans. Cybern. 45(11), 2449–2460 (2015)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Electrical Engineering and Electronic Information, Xihua University, Chengdu, 610036, People’s Republic of China

    Bo Wang

  2. School of Automation and Electrical Engineering, Qingdao University of Science and Technology, Qingdao, 266061, People’s Republic of China

    Dian Zhang & Jun Cheng

  3. Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan, 38541, Republic of Korea

    Ju H. Park

Authors
  1. Bo Wang
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  2. Dian Zhang
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  3. Jun Cheng
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  4. Ju H. Park
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Corresponding authors

Correspondence to Jun Cheng or Ju H. Park.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

This work was supported in part by the National Natural Science Foundation of China (NSFC: 61703150), the Natural Science Foundation of Shandong Provinces of China (ZR2018LC010), the Program for Innovative Research Team of the Higher Education Institutions of Hubei Province (T201812), the Natural Science Foundation of Hubei Provinces of China (2016CFB211). The work of J.H. Park was supported by Basic Science Research Programs through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number NRF-2017R1A2B2004671).

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Wang, B., Zhang, D., Cheng, J. et al. Fuzzy model-based nonfragile control of switched discrete-time systems. Nonlinear Dyn 93, 2461–2471 (2018). https://doi.org/10.1007/s11071-018-4336-5

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  • DOI: https://doi.org/10.1007/s11071-018-4336-5

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