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Global Lagrange Stability for Takagi-Sugeno Fuzzy Cohen-Grossberg BAM Neural Networks with Time-varying Delays

  • Jingfeng Wang
  • Lixin Tian
  • Zaili Zhen
Regular Papers Control Theory and Applications
  • 44 Downloads

Abstract

This paper concerns the globally exponential stability in Lagrange sense for Takagi-Sugeno (T-S) fuzzy Cohen-Grossberg BAM neural networks with time-varying delays. Based on the Lyapunov functional method and inequality techniques, two different types of activation functions which include both Lipschitz function and general activation functions are analyzed. Several sufficient conditions in linear matrix inequality form are derived to guarantee the Lagrange exponential stability of Cohen-Grossberg BAM neural networks with time-varying delays which are represented by T-S fuzzy models. Finally, simulation results demonstrate the effectiveness of the theoretical results.

Keywords

Cohen-Grossberg BAM neural networks Lagrange stability Lyapunov functional time-varying delays T-S fuzzy model 

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References

  1. [1]
    M. A. Cohen and S. Grossberg, “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,” IEEE Transactions on Systems Man & Cybernetics, vol. SMC-13, no. 5, pp. 815–826, September 1983.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J. Cao and Q. Song, “Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays,” Nonlinearity, vol.19, pp. 1601–1617, July 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    X. Li, “Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays,” Applied Mathematics and Computation, vol. 215, pp. 292–307, September 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Y. K. Li and X. Fan, “Existence and global exponential stability of almost periodic solution for Cohen-Grossberg-type BAM neural networks with variable coefficients,” Applied Mathematical Modelling, vol. 33, pp. 2114–2120, April 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    X. Li and X. Fu, “Global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays: an LMI approach,” Journal of Computational and Applied Mathematics, vol. 235, pp. 3385–3394, April 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    J. H. Park, “Robust stability of bidirectional associative memory neural networks with time delays,” Physics Letters A, vol. 349, pp. 494–499, January 2006.CrossRefGoogle Scholar
  7. [7]
    J. H. Park, C. H. Park, O. M. Kwon, and S. M. Lee, “A new stability criterion for bidirectional associative memory neural networks of neutral-type,” Applied Mathematics and Computation, vol. 199, pp. 716–722, June 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    K. Li, “Stability in impulsive Cohen-Grossberg-type BAM neural networks with time-varying delays: A general analysis,” Mathematics and Computers in Simulation vol. 215, no. 11, pp. 3970–3984, August 2010.zbMATHGoogle Scholar
  9. [9]
    K. Li, L. Zhang, X. Zhang, and Z. Li, “Stability in impulsive Cohen-Grossberg-type BAM neural networks with distributed delays,” Applied Mathematics and Computation, vol. 215, pp. 3970–3984, February 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Z. Zhang, W. Liu, and D. Zhou, “Global asymptotic stability to a generalized Cohen-Grossberg-type BAM neural networks of neutral type delays,” Neural Networks, vol. 25, pp. 94–105, January 2012.CrossRefzbMATHGoogle Scholar
  11. [11]
    Z. Zhang, G. Peng, and D. Zhou, “Periodic solution to Cohen-Grossberg-type BAM neural networks with delays on time scales,” Journal of the Franklin Institute, vol. 348, no. 10, pp. 2759–2781, December 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Z. Zhang, J. Cao, and D. Zhou, “Novel LMI-based condition on global asymptotic stability for a class of Cohen-Grossberg-type BAM networks with extended activation functions,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 6, pp. 1161–1172, April 2014.CrossRefGoogle Scholar
  13. [13]
    D. Zhou, S. Yu, and Z. Zhang, “New LMI-based condition for global exponential stability to a class of Cohen-Grossberg BAM networks with delays,” Neurocomputing, vol. 121, pp. 512–522, December 2013.CrossRefGoogle Scholar
  14. [14]
    J. Jian and B. Wang, “Global Lagrange stability for neuraltype Cohen-Grossberg BAM neural networks with mixed time-varying delays,” Mathematics and Computers in Simulation, vol. 116, no. 1, pp. 1–25, April 2015.MathSciNetCrossRefGoogle Scholar
  15. [15]
    H. M. Bao, “Existence and exponential stability of periodic solution for BAM fuzzy cohen-grossberg neural networks with mixed delays,” Neural Processing Letter, vol. 43, no. 3, pp. 871–885, June 2016.CrossRefGoogle Scholar
  16. [16]
    R. Sathy and P. Balasubramaniam, “Stability analysis of fuzzy Markovian jumping Cohen-Grossberg BAM neural networks with mixed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 2054–2064, April 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    P. Balasubramaniam and M. S. Ali, “Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays,” Mathematical and Computer Modelling, vol. 53, pp. 151–160, January 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    M. S. Ali, P. Balasubramaniam, F. A. Rihan, and S. Lakshmanan, “Stability criteria for stochastic Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with mixed time-varying delays,” Complexity, vol. 21, no. 5, pp. 143–154, December 2016.MathSciNetCrossRefGoogle Scholar
  19. [19]
    T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Transactions on Systems Man and Cybernetics, vol. SMC-15, no. 1, pp. 116–132, January-February 1985.CrossRefzbMATHGoogle Scholar
  20. [20]
    H. Yamamoto and T. Furuhashi, “A new sufficient condition for stable fuzzy control system and its design method,” Fuzzy Systems IEEE Transactions on, vol. 9, no. 4, pp. 554–569, August 2001.CrossRefGoogle Scholar
  21. [21]
    Y. Y. Hou, T. L. Liao, and J. J. Yan, “Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with timevarying delays,” IEEE Transactions on Systems Man and Cybernetics Part B, vol. 37, no. 3, pp. 720–726, June 2007.CrossRefGoogle Scholar
  22. [22]
    Y. Liu, J. H. Park, B. Z. Guo, and Y. Shu, “Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 2, pp. 1040–1045, April 2018.CrossRefGoogle Scholar
  23. [23]
    Y. Liu, B. Z. Guo, J. H. Park, and S. M. Lee, “Event-based reliable dissipative filtering for T-S fuzzy systems with asynchronous constraints,” IEEE Transactions on Fuzzy Systems, 2017. DOI:10.1109/TFUZZ.2017.2762633Google Scholar
  24. [24]
    B.Wang, J. Cheng, A. Al-Barakati, and H. M. Fardoun, “A mismatched membership function approach to sampleddata stabilization for T-S fuzzy systems with time-varying delayed signals,” Signal Processing, vol. 140, pp. 161–170, November 2017.CrossRefGoogle Scholar
  25. [25]
    J. Cheng, J. H. Park, Y. J. Liu, Z. J. Lin, and L. M. Tang, “Finite-time H¥ fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions,” Fuzzy Sets and Systems, vol. 314, pp. 99–115, May 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    J. Cheng, J. H. Park, L. Zhang, and Y. Zhu, “An asynchronous operation approach to event-triggered control for fuzzy markovian jump systems with general switching policies,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 1, pp. 6–18, February 2018.CrossRefGoogle Scholar
  27. [27]
    J. G. Jian and W. L. Jiang, “Lagrange exponential stability for fuzzy Cohen-Grossberg neural networks with timevarying delays,” Fuzzy Sets and Systems, vol. 277, pp. 65–80, October 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    S. Muralisankar and N. Gopalakrishnan, “Robust stability criteria for Takagi-Sugeno fuzzy Cohen-Grossberg neural networks of neutral type,” Neurocomputing, vol. 144, pp. 516–525, Novembe 2014.CrossRefzbMATHGoogle Scholar
  29. [29]
    M. S. Ali, P. Balasubramaniam, and Q. Zhu, “Stability of stochastic fuzzy BAM neural networks with discrete and distributed time-varying delay,” International Journal of Machine Learning and Cybernetics, vol. 8, no. 1, pp. 263–273, February 2017.CrossRefGoogle Scholar
  30. [30]
    X. X. Liao, Q. Luo, and Z. G. Zeng, “Positive invariant and global exponential attractive sets of neural networks with time-varying delays,” Neurocomputing, vol. 71, pp. 513–518, January 2008.CrossRefGoogle Scholar
  31. [31]
    Q. Luo, Z. G. Zeng, and X. X. Liao, “Global exponential stability in Lagrange sense for neutral type recurrent neural networks,” Neurocomputing, vol. 74, pp. 638–645, January 2011.CrossRefGoogle Scholar
  32. [32]
    J. G. Jian and Z. H. Zhao, “Global stability in Lagrange sense for BAM-type Cohen-Grossberg neural networks with time-varying delays,” Systems Science Control Engineering, vol. 3, no. 1, pp. 1–7, December 2014.CrossRefGoogle Scholar
  33. [33]
    J. G. Jian and B. X. Wang, “Stability analysis in Lagrange sense for a class of BAM neural networks of neutral type with multiple time-varying delays,” Neurocomputing, vol. 149, pp. 930–939, February 2015.CrossRefGoogle Scholar
  34. [34]
    L. L. Li and J. G. Jian, “Exponential convergence and Lagrange stability for impulsive Cohen-Grossberg neural networks with time-varying delay,” Journal of Computational and Applied Mathematics, vol. 277, pp. 23–35, March 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    A. L. Wu and Z. G. Zeng, “Lagrange stability of memristive neural networks with discrete and distributed delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 4, pp.690–703, April 2014.MathSciNetCrossRefGoogle Scholar
  36. [36]
    J. F. Wang, L. X. Tian, “Global Lagrange stability for inertial neural networks with mixed time-varying delays,” Neurocomputing, vol. 235, pp. 140–146, April 2017.CrossRefGoogle Scholar
  37. [37]
    Z. W. Tu and J. D. Cao, “Global lagrange stability of complex-valued neural networks of neutral type with timevarying delays,” Complexity, vol. 21, no. S2, pp. 438–450, November-December 2016.MathSciNetCrossRefGoogle Scholar
  38. [38]
    H. Huang, D. W. C. Ho, and J. Lam, “Stochastic stability analysis of fuzzy Hopfield neural networks with timevarying delays,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 52, no. 25, pp. 251–255, May 2005.CrossRefGoogle Scholar
  39. [39]
    S. Y. Xu and J. Lam, “A new approach to exponential stability analysis of neural networks with time-varying delays,” Neural Networks, vol. 19, no. 1, pp. 76–83, January 2006.CrossRefzbMATHGoogle Scholar
  40. [40]
    X. Li and R. Rakkiyappan, “Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 6, pp. 1515–1523, June 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    S. Boyd, “Linear matrix inequalities in system and control theory,” Proceedings of the IEEE International Conference on Robotics and Automation, vol. 85, no. 5, pp. 789–799, September 1995.Google Scholar
  42. [42]
    J. G. Jian, D. M. Kong, H. G. Luo, and X. X. Liao, “Exponential stability of differential systems with separated variables and time delays,” Journal of Central South University of Technology, vol. 36, no. 2, pp. 282–287, April 2005.Google Scholar
  43. [43]
    W. Zhang, Y. Tang, X. Wu, and J. A. Fang, “Synchronization of nonlinear dynamical networks with heterogeneous impulses,” IEEE Transactions on Circuits and Systems I Regular Papers, vol.61, no. 4, pp. 1220–1228, April 2014.CrossRefGoogle Scholar
  44. [44]
    Q. K. Song, H. Yan, Z. J. Zhao, and Y. R. Liu, “Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects,” Neural Networks, vol. 79, pp. 108–116, July 2016.CrossRefGoogle Scholar
  45. [45]
    L. M. Wang, Y. Shen, and Y. Sheng, “Finite-time robust stabilization of uncertain delayed neural networks with discontinuous activations via delayed feedback control,” Neural Networks, vol. 76, pp. 46–54, April 2016.CrossRefGoogle Scholar
  46. [46]
    S. J. Yang, C. D. Li, and T. W. Huang, “Exponential stabilization and synchronization for fuzzy model of memristive neural networks by periodically intermittent control,” Neural Networks, vol. 75, pp. 162–172, March 2016.CrossRefGoogle Scholar
  47. [47]
    W. Zhang, Y. Tang, T. Huang, and J. Kurths, “Sampleddata consensus of linear multi-agent systems with packet losses,” IEEE Transactions Neural Networks and Learning Systems, vol. 28, no. 11, pp. 2516–2527, November 2017.MathSciNetCrossRefGoogle Scholar
  48. [48]
    D. Q. Zeng, R. M. Zhang, Y. J. Liu, and S. M. Zhong, “Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach,” Applied Mathematics and Computation, vol. 315, pp. 34–46, December 2017.MathSciNetCrossRefGoogle Scholar
  49. [49]
    R. M. Zhang, D. Q. Zeng, S. M. Zhong, and Y. B. Yu, “Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays,” Applied Mathematics and Computation, vol. 310, pp. 57–74, October 2017.MathSciNetCrossRefGoogle Scholar
  50. [50]
    R. M. Zhang, D. Q. Zeng, and S. M. Zhong, “Novel master-slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control,” Journal of the Franklin Institute, vol. 354, pp. 4930–4954, August 2017.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Faculty of ScienceJiangsu UniversityZhenjiangChina
  2. 2.School of Mathematical SciencesNanjing Normal UniversityNanjingChina
  3. 3.School of Faculty of ScienceJiangsu UniversityZhenjiangChina

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