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New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays

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Abstract

This letter considers the robust exponential stability of uncertain stochastic neural networks with mixed time-varying delays. By using Lyapunov–Krasovskii functional and Itô’s differential formula, several new sufficient conditions guaranteeing the global robust exponential stability are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and less conservativeness of our results.

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References

  1. Haykin S (1994) Neural networks. Prentice-Hall, NJ

    MATH  Google Scholar 

  2. Young S, Scott P, Nasrabadi N (1997) Object recognition using multilayer Hopfield neural network. IEEE Trans Image Proc 6: 357–372

    Article  Google Scholar 

  3. Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Ciruits Syst I 52: 417–426

    Article  MathSciNet  Google Scholar 

  4. Xu S, Lam J, Ho D, Zou Y (2005) Delay-dependent exponential stability for a class of neural networks with time delays. J Comput Appl Math 183: 16–28

    Article  MATH  MathSciNet  Google Scholar 

  5. Liu X, Dickson R (2001) Stability analysis of Hopfield neural networks with uncertainty. Math Compu Modell 34: 353–363

    Article  MATH  MathSciNet  Google Scholar 

  6. Liu X, Teo K, Xu B (2005) Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. IEEE Trans Neural Netw 16: 1329–1339

    Article  Google Scholar 

  7. Rong L, Chen T (2006) New results on the robust stability of Cohen–Grossberg neural networks with delays. Neural Process Lett 24: 193–202

    Article  MATH  Google Scholar 

  8. Cao J, Wang J (2004) Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Netw 17: 379–390

    Article  MATH  Google Scholar 

  9. He Y, Liu G, Rees D (2007) New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans Neural Netw 18: 310–314

    Article  Google Scholar 

  10. He Y, Liu G, Rees D, Wu M (2007) Stability analysis for neural networks with time-varying interval delay. IEEE Trans Neural Netw 18: 1850–1854

    Article  Google Scholar 

  11. Li C, Liao X, Wong K (2006) Delay-dependent and delay-independent stability criteria for cellular neural networks with delays. Int J Bifurcation Chaos 16: 3323–3340

    Article  MATH  MathSciNet  Google Scholar 

  12. Liao X, Wong K, Yang S (2004) Stability analysis for delayed cellular neural networks based on linear matrix inequality approach. Int J Bifurcation Chaos 14: 3377–3384

    Article  MATH  MathSciNet  Google Scholar 

  13. Rong L, Chen T (2006) New results on the robust stability of Cohen–Grossberg neural networks with delays. Neural Process Lett 24: 193–202

    Article  MATH  Google Scholar 

  14. He Y, Wu M, She J, Liu G (2004) Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Systems Control Lett 51: 57–65

    Article  MATH  MathSciNet  Google Scholar 

  15. Blythe S, Mao X, Liao X (2001) Stability of stochastic delay neural networks. J Franklin Inst 338: 481–495

    Article  MATH  MathSciNet  Google Scholar 

  16. Yu W, Cao J (2007) Robust control of uncertain stochastic recurrent neural networks with time-varying delay. Neural Process Lett 26: 101–119

    Article  Google Scholar 

  17. Zhu E, Zhang H, Wang Y, Zou J, Yu Z, Hou Z (2007) Pth moment exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays. Neural Process Lett 26: 191–200

    Article  MATH  Google Scholar 

  18. Zhang J, Shi P, Qiu J (2007) Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays. Nonlinear Anal Real World Appl 8: 1349–1357

    Article  MATH  MathSciNet  Google Scholar 

  19. Wang Z, Shu H, Fang J, Liu X (2006) Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal Real World Appl 7: 1119–1128

    Article  MATH  MathSciNet  Google Scholar 

  20. Su W, Chen Y (2009) Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays. Commun Nonlinear Sci Numer Simul 14: 1576–1581

    Article  MathSciNet  Google Scholar 

  21. Qiu J, Yang H, Xia Y, Zhang J (2007) Mean square exponential stability of uncertain stochastic Hopfield neural networks with interval time-varying delays. LNCS 4682: 110–119

    Google Scholar 

  22. Qiu J, Gao Z, Wang J, Shi P (2008) Robust stability criteria for uncertain stochastic cellular neural networks with time delays. In Second Int Conference on Innovative Comp Info Cont ICICIC 2007, art no 4428198

  23. 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: 814–820

    Article  Google Scholar 

  24. Wang Z, Lauria S, Fang J, Liu X (2007) Exponential stability of uncertain stochastic neural networks with mixed time delays. Chaos Solitons Fractals 32: 62–72

    Article  MATH  MathSciNet  Google Scholar 

  25. Wang Z, Fang J, Liu X (2008) Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fractals 36: 388–396

    Article  MATH  MathSciNet  Google Scholar 

  26. Zhang J, Shi P, Qiu J, Yang H (2008) A new criterion for exponential stability of uncertain stochastic neural networks with mixed delays. Mathe Comp Modell 47: 1042–1051

    Article  MATH  MathSciNet  Google Scholar 

  27. Huang H, Feng G (2007) Delay-dependent stability for uncertain stochastic neural networks with time-varying delay. Phys Lett A 381: 93–103

    Google Scholar 

  28. Yu J, Zhang K, Fei S (2009) Further results on mean square exponential stability of uncertain stochastic delayed neural networks. Commun Nonlinear Sci Numer Simul 14: 1582–1589

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  30. Li H, Chen B, Zhou Q, Fang S (2008) Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays. Phys Lett A 372: 3385–3394

    Article  MathSciNet  Google Scholar 

  31. Yue D, Han Q (2005) Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and markovian switching. IEEE Trans Autom Control 50: 217–222

    Article  MathSciNet  Google Scholar 

  32. Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear Matrix inequalities in system and control theory. SIAM, Philadephia

    MATH  Google Scholar 

  33. Wang Y, Xie L, de Souza C (1992) Robust control of a class of uncertain nonlinear system. Syst Contr Lett 19: 139–149

    Article  Google Scholar 

  34. Gu K, Kharitonov V, Chen J (2003) Stability of time-delay systems. Birkhäuser, Boston

    MATH  Google Scholar 

  35. Mao X, Koroleva N, Rodkina A (1998) Robust stability of uncertain stochastic diffrential delay equations. Systems Control Lett 35: 325–336

    Article  MATH  MathSciNet  Google Scholar 

  36. Jing X, Tan D, Wang Y (2004) An LMI approach to stability of systems with severe time-delay. IEEE Trans Autom Control 49: 1192–1195

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Computer and Information, Hohai University, Changzhou, 213022, China

    Mingang Hua & Juntao Fei

  2. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Mingang Hua & Xinzhi Liu

  3. College of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Feiqi Deng

Authors
  1. Mingang Hua
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  2. Xinzhi Liu
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  3. Feiqi Deng
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  4. Juntao Fei
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Correspondence to Xinzhi Liu.

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Hua, M., Liu, X., Deng, F. et al. New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays. Neural Process Lett 32, 219–233 (2010). https://doi.org/10.1007/s11063-010-9152-y

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