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Robust exponential stability analysis for interval Cohen–Grossberg type BAM neural networks with mixed time delays

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Abstract

In this paper, the robust exponential stability issue for the interval Cohen–Grossberg type BAM neural networks with nonsmooth behaved functions and mixed time delays is investigated. Firstly, based on Homomorphic mapping theory and nonsmooth analysis approach, the existence and uniqueness of the equilibrium point are proved. Secondly, by applying linear matrix inequality (LMI), free-weighting matrix technique, and available Lyapunov-Krasovskii functional method, some delay-dependent conditions are achieved in terms of LMIs to ensure the considered neural network to be globally robustly exponentially stable. The results obtained in this paper are little conservative compared with the previous results in the literature. Finally, two simulation examples are given to illustrate the validity of the theoretical results.

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References

  1. Raja R, Sakthivel R, Marshal Anthoni S, Kim H (2011) Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays. Int J Appl Math Comput Sci 21:127–135

    Article  MATH  MathSciNet  Google Scholar 

  2. Sakthivel R, Mathiyalagan K, Marshal Anthoni S (2011) Design of a passification controller for uncertain fuzzy Hopfield neural networks with time-varying delays. Physica Scripta 84(4) art. no. 045024

    Google Scholar 

  3. Vidhya C, Balasubramaniam P (2011) Robust stability of uncertain Markovian jumping stochastic Cohen–Grossberg type BAM neural networks with time-varying delays and reaction diffusion terms. Neural Parallel Sci Comput 19(1–2):181–196

    MATH  MathSciNet  Google Scholar 

  4. Sakthivel R, Raja R, Marshal Anthoni S (2011) Exponential stability for delayed stochastic bidirectional associative memory neural networks with Markovian jumping and impulses. J Optim Theory Appl 150:166–187

    Article  MATH  MathSciNet  Google Scholar 

  5. Balasubramaniam P, Syed Ali M (2011) Stability analysis of Takagi-Sugeno fuzzy Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. Math Comput Model 53(1–2):151–160

    Article  MATH  MathSciNet  Google Scholar 

  6. Syed Ali M, Balasubramaniam P (2009) Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays. Expert Syst Appl 36(7):10583-10588

    Article  Google Scholar 

  7. Sakthivel R, Samidurai R, Marshal Anthoni S (2010) New exponential stability criteria for stochastic BAM neural networks with impulses. Physica Scripta 82:045802

    Google Scholar 

  8. Mathiyalagan K, Sakthivel R, Marshal Anthoni S (2012) New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays. Commun Nonlinear Sci Numer Simul 17:1392–1407

    Article  MATH  MathSciNet  Google Scholar 

  9. Wu H, Tao F, Qin L, Shi R, He L (2011) Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions. Nonlinear Dyn 66(4):479–487

    Article  MATH  MathSciNet  Google Scholar 

  10. Liu H, Chen G (2007) Delay-dependent stability for neural networks with time-varying delay. Chaos Solitons Fractals 33(1):171–177

    Article  MATH  MathSciNet  Google Scholar 

  11. Wu H, Xu G, Wu C, Li N, Wang K, Guo Q (2012) Stability in switched Cohen–Grossberg neural networks with mixed time delays and non-Lipschitz activation functions. Discrete Dyn Nat Soc art. no. 435402

  12. Boehm O, Hardoon DR, Manevitz LM (2011) Classifying cognitive states of brain activity via one-class neural networks with feature selection by genetic algorithms. Int J Mach Learn Cybern 2(3):125–134

    Article  Google Scholar 

  13. Zheng H, Wang H (2012) Improving pattern discovery and visualisation with self-adaptive neural networks through data transformations. Int J Mach Learn Cybern 3(3):173–182

    Article  Google Scholar 

  14. Sarlin P (2012) Visual tracking of the millennium development goals with a fuzzified self-organizing neural network. Int J Mach Learn Cybern 3(3):233–245

    Article  Google Scholar 

  15. Tong DL, Mintram R (2010) Genetic algorithm-neural network (GANN): a study of neural network activation functions and depth of genetic algorithm search applied to feature selection. Int J Mache Learn Cybern 1(1–4):75–87

    Article  Google Scholar 

  16. Kosko B (1987) Adaptive bidirectional associative memories. Appl Optim 26(23):4947–4960

    Article  Google Scholar 

  17. Yu W, Yao L (2007) Global robust stability of neural networks with time varying delays. J Comput Appl Math 206:679–687

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang L, Shi B (2009) Global exponential stability of Cohen–Grossberg neural netvorks with Variable delays. Appl Math J Chin Univ 24(2):167–174

    Article  MATH  Google Scholar 

  19. Zhang Z, Yang Y, Huang Y (2011) Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays. Neural Netw 24:457–465

    Article  MATH  Google Scholar 

  20. Li T, Fei S, Guo Y, Zhu Q (2009) Stability analysis on Cohen–Grossberg neural networks with both time-varying and continuously distributed delays. Nonlinear Anal Real World Appl 10(4):2600–2612

    Article  MATH  MathSciNet  Google Scholar 

  21. Chen A, Cao J (2007) Periodic bi-directional Cohen–Grossberg neural networks with distributed delays. Nonlinear Anal 66:2947–2961

    Article  MATH  MathSciNet  Google Scholar 

  22. Feng C, Plamondon R (2003) Stability analysis of bidirectional associative memory networks with time delays. IEEE Trans Neural Netw 14:1560–1565

    Article  Google Scholar 

  23. Li K, Zeng H (2010) Stability in impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays. A general analysis. Math Comput Simul 80:2329–2349

    Google Scholar 

  24. Faydasicok O, Arik S (2012) Robust stability analysis of a class of neural networks with discrete time delays. Neural Netw 29–30:52–59

    Article  Google Scholar 

  25. Arik S (2005) Global robust stability analysis of neural networks with discrete time delays. Chaos Solitons and Fractals 26:1407–1414

    Article  MATH  MathSciNet  Google Scholar 

  26. Senan S, Arik S (2009) New results for global robust stability of bidirectional associative memory neural networks with multiple time delays. Chaos Solitons and Fractals 41(4):2106–2114

    Article  MATH  MathSciNet  Google Scholar 

  27. Wang Ch, Shen Y (2011) Improved delay-dependent robust stability criteria for uncertain time delay systems. Appl Math Comput 218:2880–2888

    Article  MATH  MathSciNet  Google Scholar 

  28. Liu L, Han Z, Li W (2009) Global stability analysis of interval neural networks with discrete and distributed delays of neutral type. Expert Syst Appl 36(3):7328–7331

    Article  Google Scholar 

  29. Hua C, Long C, Guan X (2006) New results on stability analysis of neural networks with time-varying delays. Phys Lett A352(4–5):335–340

    Article  Google Scholar 

  30. Zhang Zh, Liu W, Zhou D (2012) Global asymptotic stability to a generalized CohenCGrossberg BAM neural networks of neutral type delays. Neural Netw 25:94–105

    Article  MATH  Google Scholar 

  31. Song Q, Cao J (2007) Global robust stability of interval neural networks with multiple time-varying delays. Math Comput Simul 74(1):38–46

    Article  MATH  MathSciNet  Google Scholar 

  32. Chen W, Lu X (2008) Mean square exponential stability of uncertain stochastic delayed neural networks. Phys Lett A372:1061–1069

    Article  Google Scholar 

  33. Deng F, Hua M, Liu X, Peng Y, Fei J (2011) Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays. Neurocomputing 74:1503–1509

    Article  Google Scholar 

  34. Lian J, Zhang K (2011) Exponential stability for switched Cohen–Grossberg neural networks with average dwell time. Nonlinear Dyn 63:331–343

    Article  MathSciNet  Google Scholar 

  35. He Y, Wang Q, Xie L, Chong L (2007) Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans Autom Control 52:293–299

    Article  Google Scholar 

  36. Zhang Y, Yue D, Tian E (2009) New stability criteria of neural networks with interval time-varying delay: a piecewise delay method. Appl Math Comput 208:249–259

    Article  MATH  MathSciNet  Google Scholar 

  37. Sathy R, Balasubramaniam P (2011) Stability analysis of fuzzy Markovian jumping Cohen–Grossberg BAM neural networks with mixed time-varying delays. Commun Nonlinear Sci Numer Simul 16(4):2054–2064

    Article  MATH  MathSciNet  Google Scholar 

  38. Nie X, Cao J (2009) Stability analysis for the generalized Cohen–Grossberg neural networks with inverse Lipschitz neuron activations. Comput Math Appl 57(9):1522–1536

    Article  MATH  MathSciNet  Google Scholar 

  39. Sakthivel R, Arunkumar A, Mathiyalagan K, Marshal Anthoni S (2011) Robust passivity analysis of fuzzy Cohen–Grossberg BAM neural networks with time-varying delays. Appl Math Comput 218:3799–3809

    Article  MATH  MathSciNet  Google Scholar 

  40. Rockafellar RT, Wets RJB (1998) Variational analysis, vol 317. Springer, Berlin

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Acknowledgments

This work was supported by the Natural Science Foundation of China (71071133), (61273004) and the Hebei Province Education Foundation of China (2009157).

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Authors and Affiliations

  1. Department of Applied Mathematics, Yanshan University, Qinhuangdao, 066001, China

    Qingqing He, Deyou Liu, Huaiqin Wu & Sanbo Ding

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  1. Qingqing He
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  2. Deyou Liu
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  3. Huaiqin Wu
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  4. Sanbo Ding
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Correspondence to Huaiqin Wu.

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He, Q., Liu, D., Wu, H. et al. Robust exponential stability analysis for interval Cohen–Grossberg type BAM neural networks with mixed time delays. Int. J. Mach. Learn. & Cyber. 5, 23–38 (2014). https://doi.org/10.1007/s13042-013-0186-0

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  • DOI: https://doi.org/10.1007/s13042-013-0186-0

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