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Improved Stability Results for Stochastic Cohen–Grossberg Neural Networks with Discrete and Distributed Delays

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Abstract

This paper is concerned with the exponential stability problem for a class of stochastic Cohen–Grossberg neural networks with discrete and unbounded distributed time delays. By applying the Jensen integral inequality and the generalized Jensen integral inequality, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results.

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References

  1. Arnold L (1972) Stochastic differential equations: theory and applications. Wiley, New York

    Google Scholar 

  2. Boyd S, Ghaoui LEI, Feron E, Balakrishnan V (1994) Linear matrix inequality in system and control theory. SIAM, Philadelphia

    Book  Google Scholar 

  3. Chen W, Lu X (2008) Mean square exponential stability of uncertain stochastic delayed neural networks. Phys Lett A 372: 1061–1069

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen P, Huang C, Liang X (2010) Stochastic stability of Cohen-Grossberg neural networks with unbounded distributed delays. Electron J Differ Equ 42: 1–11

    MathSciNet  MATH  Google Scholar 

  5. Fu J, Zhang H, Ma T (2009) Delay-probability-distribution-dependent robust stability analysis for stochastic neural networks with time-varying delay. Prog Nat Sci 19: 1333–1340

    Article  MathSciNet  Google Scholar 

  6. Gu K, Kharitonov VL, Chen J (2003) Stability of time-delay systems. Birkhauser, Boston

    Book  MATH  Google Scholar 

  7. Haykin S (1998) Neural networks: a comprehensive foundation. Prentice-Hall, Upper Saddle River

    Google Scholar 

  8. Kwon OM, Park JH (2009) Improved delay-dependent stability criterion for neural networks with time-varying delays. Phys Lett A 373(5): 529–535

    Article  MathSciNet  MATH  Google Scholar 

  9. 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: 2600–2612

    Article  MathSciNet  MATH  Google Scholar 

  10. Li T, Song A, Fei S (2009) Robust stability of stochastic Cohen-Grossberg neural networks with mixed time-varying delays. Neurocomputing 73: 542–551

    Article  Google Scholar 

  11. Liao X, Mao X (1996) Exponential stability and instability of stochastic neural networks. Stoch Anal Appl 14: 165–185

    Article  MathSciNet  MATH  Google Scholar 

  12. Lou X, Cui B (2007) Global exponential stability analysis of delayed Cohen-Grossberg neural networks with distributed delays. Int J Syst Sci 38(7): 601–609

    Article  MathSciNet  MATH  Google Scholar 

  13. Mao X (1997) Stochastic differential equations and their applications. Horwood, Chichester

    MATH  Google Scholar 

  14. Singh V (2008) A new criterion for global robust stability of interval delayed neural networks. J Comput Appl Math 221(1): 219–225

    Article  MathSciNet  MATH  Google Scholar 

  15. Song Q (2008) Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach. Neurocomputing 71(13–15): 2823–2830

    Article  Google Scholar 

  16. Sun J, Liu GP, Chen J, Rees D (2009) Improved stability criteria for neural networks with time-varying delay. Phys Lett A 373: 342–348

    Article  MATH  Google Scholar 

  17. Tang Y, Fang J, Miao Q (2009) On the exponential synchronization of stochastic jumping chaotic neural networks with mixed delays and sector-bounded non-linearities. Neurocomputing 72: 1694–1701

    Article  Google Scholar 

  18. Wang Z, Liu Y, Li M, Liu X (2006) Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 17(3): 814–820

    Article  Google Scholar 

  19. Wang B, Zhong S, Liu X (2008) Asymptotical stability criterion on neural networks with multiple time-varying delays. Appl Math Comput 195(2): 809–818

    Article  MathSciNet  MATH  Google Scholar 

  20. Wu W, Cui BT (2008) Global robust exponential stability of delayed neural networks. Chaos Solitons Fractals 35(4): 747–754

    Article  MathSciNet  MATH  Google Scholar 

  21. Wu Y, Wu Y, Chen Y (2009) Mean square exponential stability of uncertain stochastic neural networks with time-varying delay. Neurocomputing 72: 2379–2384

    Article  Google Scholar 

  22. Xiong W, Cao J (2005) Absolutely exponential stability of Cohen-Grossberg neural networks with unbounded delays. Neurocomputing 68: 1–12

    Article  Google Scholar 

  23. Xiang H, Cao J (2009) Almost periodic solution of Cohen-Grossberg neural networks with bounded and unbounded delays. Nonlinear Anal Real World Appl 10(4): 2407–2419

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang H, Wang Z (2007) Global asymptotic stability of delayed cellular neural networks. IEEE Trans Neural Netw 18(3): 947–950

    Article  Google Scholar 

  25. Zhang H, Wang Y (2008) Stability analysis of markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19(2): 366–370

    Article  Google Scholar 

  26. Zhang H, Wang Z, Liu D (2007) Robust exponential stability of cellular neural networks with multiple time varying delays. IEEE Trans Circuits Syst II 54(8): 730–734

    Article  Google Scholar 

  27. Zhang H, Wang Z, Liu D (2008) Robust stability analysis for interval Cohen-Grossberg neural networks with unknown time-varying delays. IEEE Trans Neural Netw 19(11): 1942–1955

    Article  Google Scholar 

  28. Zhang H, Wang Z, Liu D (2008) Global asymptotic stability of recurrent neural networks with multiple time-varying delays. IEEE Trans Neural Netw 19(5): 855–873

    Article  MathSciNet  Google Scholar 

  29. 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(1): 249–259

    Article  MathSciNet  MATH  Google Scholar 

  30. Zhang B, Xu S, Zong G, Zou Y (2009) Delay-dependent exponential stability for uncertain stochastic Hopfield neural networks with time-varying delays. IEEE Trans Circuits Syst I 56(6): 1241–1247

    Article  MathSciNet  Google Scholar 

  31. Zhang H, Liu Z, Huang GB, Wang Z (2010) Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans Neural Netw 21(1): 91–106

    Article  Google Scholar 

  32. Zhao H, Chen L, Mao Z (2008) Existence and stability of almost periodic solution for Cohen-Grossberg neural networks with variable coefficients. Nonlinear Anal Real World Appl 9: 663–673

    Article  MathSciNet  MATH  Google Scholar 

  33. Zheng CD, Jing XT, Wang Z, Feng J (2010) Further results for robust stability of cellular neural networks with linear fractional uncertainty. Commun Nonlinear Sci Numer Simul 15(10): 3046–3057

    Article  MathSciNet  MATH  Google Scholar 

  34. Zhu XL, Yang GH (2008) New delay-dependent stability results for neural networks with time-varying delay. IEEE Trans Neural Netw 19(10): 1783–1791

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Science, Dalian Jiaotong University, Dalian, 116028, People’s Republic of China

    Cheng-De Zheng & Qi-He Shan

  2. School of Information Science and Engineering, Northeastern University, Shenyang, 110004, People’s Republic of China

    Zhanshan Wang

Authors
  1. Cheng-De Zheng
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  2. Qi-He Shan
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  3. Zhanshan Wang
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Correspondence to Cheng-De Zheng.

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Zheng, CD., Shan, QH. & Wang, Z. Improved Stability Results for Stochastic Cohen–Grossberg Neural Networks with Discrete and Distributed Delays. Neural Process Lett 35, 103–129 (2012). https://doi.org/10.1007/s11063-011-9206-9

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  • DOI: https://doi.org/10.1007/s11063-011-9206-9

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