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Global Exponential Convergence of Fuzzy Cellular Neural Networks with Leakage Delays, Distributed Delays and Proportional Delays

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Abstract

In this paper, a class of fuzzy cellular neural networks (FCNNs) with leakage delays, distributed delays and proportional delays are considered. Using the differential inequality strategy, some sufficient criteria which ensure the global exponential convergence of the FCNNs with leakage delays, distributed delays and proportional delays are established. Numerical simulations are given to explain the obtained analytical results. The derived conclusions of this article are new and complement some earlier publications.

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References

  1. P. Balasubramaniam, M.-S. Ali, S. Arik, Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays. Expert Syst. Appl. 37(12), 7737–7744 (2010)

    Article  Google Scholar 

  2. P. Balasubramaniam, M. Kalpana, R. Rakkiyappan, Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst. Signal Process. 30(6), 1595–1616 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Balasubramanianm, V. Vembarasan, R. Rakkiyappan, Leakage delay in T–S Fuzzy cellular neural networks. Neural Process. Lett. 33, 111–136 (2011)

    Article  Google Scholar 

  4. G.-A. Derfel, On the behaviour of the solutions of functional and functional-differential equations with several deviating arguments. Ukr. Math. J. 34, 286–291 (1982)

    Article  MATH  Google Scholar 

  5. G.-A. Derfel, Kato problem for functional-differential equations and difference Schrodinger operator. Oper. Theor. 46, 319–321 (1990)

    MathSciNet  MATH  Google Scholar 

  6. Z. Feng, W.-X. Zheng, On extended dissipativity of discrete-time neural networks with time delay. IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3293–3300 (2015)

    Article  MathSciNet  Google Scholar 

  7. L. Fox, D.F. Ockendon, A.B. Tayler, On a functional-differential equations. J. Inst. Math. Appl. 8(3), 271–307 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Gao, Q.-R. Wang, L.-W. Zhang, Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales. Appl. Math. Comput. 237, 639–649 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Z.-D. Huang, Almost periodic solutions for fuzzy cellular neural networks with multi-proportional dealys. Int. J. Mach. Learn. Cybern. 78(4), 1–9 (2016)

    Google Scholar 

  10. Z.-D. Huang, Almost periodic solutions for fuzzy cellular neural networks with time-varying dealys. Neural Comput. Appl. (In press) (2016)

  11. J.-G. Jian, P. Wan, Global exponential convergence of generalized chaotic systems with multiple time-varying and finite distributed delays. Phys. A 431, 152–165 (2015)

    Article  MathSciNet  Google Scholar 

  12. Y.-K. Li, C. Wang, Almost periodic solutions of shunting inhibitory cellular neural networks on time scales. Commun. Nonlinear Sci. Numer. Simul. 17(8), 3258–3266 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Y.-K. Li, L. Yang, W.-Q. Wu, Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales. Neurocomputing 149, 536–545 (2015)

    Article  Google Scholar 

  14. B.-W. Liu, Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191, 352–355 (2016)

    Article  Google Scholar 

  15. B.-W. Liu, Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal. Real World Appl. 14(1), 559–566 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. B.-W. Liu, Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process. Lett. 42(1), 233–256 (2015)

    Article  Google Scholar 

  17. S.-Y. Niu, H.-J. Jiang, Z.-D. Teng, Periodic oscillation of FCNNs with distributed delays and variable coefficients. Nonlinear Anal. Real World Appl. 10, 1540–1554 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. J.-R. Ockendon, A.-B. Tayler, The dynamics of a current collection system for an electric locomotive. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 322(1551), 447–468 (1971)

    Article  Google Scholar 

  19. H.-H. Pan, W.-C. Sun, H.-J. Gao, X.-J. Jing, Disturbance observer based adaptive tracking control with actuator saturation and its application. IEEE Trans. Autom. Sci. Eng. 13(2), 868–875 (2016)

    Article  Google Scholar 

  20. H.-H. Pan, W.-C. Sun, H.-J. Gao, O. Kaynak, F. Alsaadi, T. Hayat, Robust adaptive control of non-linear time-delay systems with saturation constraints. IET Control Theory Appl. 9(1), 103–113 (2015)

    Article  MathSciNet  Google Scholar 

  21. H.-H. Pan, W.-C. Sun, H.-J. Gao, J.-Y. Yu, Finite-time stabilization for vehicle active suspension systems with hard constraints. IEEE Trans. Intell. Transp. Syst. 16(5), 1–10 (2015)

    Article  Google Scholar 

  22. S.-T. Qin, J. Wang, X.-P. Xue, Convergence and attractivity of memristor-based cellular neural networks with time delays. Neural Netw. 63, 223–233 (2015)

    Article  MATH  Google Scholar 

  23. R. Rakkiyappan, S. Lakshmanan, R. Sivasamy, C.-P. Lim, Leakage-delay-dependent stability analysis of Markovian jumping linear systems with time-varying delays and nonlinear perturbations. Appl. Math. Modell. 40(7–8), 5026–5043 (2016)

    Article  MathSciNet  Google Scholar 

  24. S. Senthilraj, R. Raja, Q.-X. Zhu, R. Samidurai, Z.-S. Yao, Exponential passivity analysis of stochastic neural networks with leakage, distributed delays and Markovian jumping parameters. Neurocomputing 175, 401–410 (2016)

    Article  MATH  Google Scholar 

  25. Q.-K. Song, Z.-J. Zhao, Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing 171, 179–184 (2016)

    Article  Google Scholar 

  26. X.-L. Song, X. Xin, W.-P. Huang, Exponential stability of delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions. Neural Netw. 29–30, 80–90 (2012)

    Article  MATH  Google Scholar 

  27. X.-L. Song, P. Zhao, Z.-W. Xing, J.-G. Peng, Global asymptotic stability of CNNs with impulses and multi-proportional delays. Math. Methods Appl. Sci. 39(4), 722–733 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. I.-M. Stamova, R. Ilarionov, On global exponential stability for impulsive cellular neural networks with time-varying delays. Comput. Math. Appl. 59(11), 3508–3515 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. W.-C. Sun, H.-H. Pan, H.-J. Gao, Filter-based adaptive vibration control for active vehicle suspensions with electro-hydraulic actuators. IEEE Trans. Veh. Technol. 65(6), 4619–4626 (2016)

    Article  Google Scholar 

  30. S. Tyagi, S. Abbas, M. Pinto, D. Sepúlveda, Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals. Comput. Math. Appl. (In press) (2016)

  31. A.-L. Wu, Z.-G. Zeng, J.N. Zhang, Global exponential convergence of periodic neural networks with time-varying delays. Neurocomputing 78(1), 149–154 (2012)

    Article  Google Scholar 

  32. C.-J. Xu, Existence and exponential stability of anti-periodic solution in cellular neural networks with time-varying delays and impulsive effects. Electron. J. Differ. Equ. 2016(2), 1–14 (2016)

    MathSciNet  Google Scholar 

  33. C.-J. Xu, P.-L. Li, Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms. J. Nonliner Sci. Appl. 9(3), 1285–1305 (2016)

    MathSciNet  MATH  Google Scholar 

  34. C.-J. Xu, P.-L. Li, Y.-C. Pang, Exponential stability of almost periodic solutions for memristor-based neural networks with distributed leakage delays. Neural Comput. 28(12), 2726–2756 (2016)

    Article  Google Scholar 

  35. C.-J. Xu, Y.-S. Wu, On almost automorphic solutions for cellula neural networks with time-varying delays in leakage terms on time scales. J. Intell. Fuzzy Syst. 30, 423–436 (2016)

    Article  MATH  Google Scholar 

  36. C.-J. Xu, Q.-M. Zhang, Y.-S. Wu, Existence and exponential stability of periodic solution to fuzzy cellular neural networks with distributed delays. Int. J. Fuzzy Syst. 18(1), 41–51 (2016)

    Article  MathSciNet  Google Scholar 

  37. C.-J. Xu, Q.-M. Zhang, Y.S. Wu, Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays. Netw. Comput. Neural Syst. 25(4), 168–192 (2014)

    Google Scholar 

  38. L.-G. Yao, Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator. Neural Process. Lett. (In press) (2016)

  39. Y.-H. Yu, Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl. Math. Comput. 285, 1–7 (2016)

    MathSciNet  Google Scholar 

  40. W.-G. Yang, Periodic solution for fuzzy Cohen–Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients. Neural Process. Lett. 40(1), 51–73 (2014)

    Article  Google Scholar 

  41. T. Yang, L.-B. Yang, The global stability of fuzzy cellular neural networks. IEEE Trans. Circuits Syst. I 43(10), 880–883 (1996)

    Article  MathSciNet  Google Scholar 

  42. C.-Z. Zhang, G. Feng, J.-B. Qiu, W.-A. Zhang, T–S fuzzy-model-based piecewise \(\text{ H }_{\infty }\) output feedback controller design for networked nonlinear systems with medium access constraint. Fuzzy Set. Syst. 248, 86–105 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Nos. 61673008, 11261010) and Project of High-level Innovative Talents of Guizhou Province ([2016]5651).

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Correspondence to Changjin Xu.

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Xu, C., Li, P. Global Exponential Convergence of Fuzzy Cellular Neural Networks with Leakage Delays, Distributed Delays and Proportional Delays. Circuits Syst Signal Process 37, 163–177 (2018). https://doi.org/10.1007/s00034-017-0557-y

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  • DOI: https://doi.org/10.1007/s00034-017-0557-y

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