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Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay

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Abstract

In this paper, robust control of uncertain stochastic recurrent neural networks with time-varying delay is considered. A novel control method is given by using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several delay-independent and delay-dependent sufficient conditions are then further derived to ensure the global asymptotical stability in mean square for the uncertain stochastic recurrent neural networks, and the estimation gains can also be obtained. Numerical examples are constructed to verify the theoretical analysis in this paper.

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References

  1. Niu Y, Wang X (2004) Delay-dependent robust control for a class of nonlinear state-delayed systems. Proceedings of the 5th World Congress on Intelligent Control and Automation pp 907–910

  2. Kwon OM and Park JH (2004). On improved delay-dependent robust control for uncertain time-delay systems. IEEE Trans Automat Contr 49(11): 1991–1995

    Article  Google Scholar 

  3. Chen J (2004). Robust control for uncertain neutral systems with time-delays in state and control input via LMI and GAs. Appl Math and Comput 157: 535–548

    Article  MATH  Google Scholar 

  4. Liao XF, Wong KW, Wu Z and Chen G (2001). Novel robust stability criteria for interval-delayed Hopfield neural networks. IEEE Trans Circuits Syst I 48(11): 1355–1359

    Article  MATH  Google Scholar 

  5. Singh V (2005). Global robust stability of delayed neural networks: an LMI approach. IEEE Trans Circuits Syst II 52(1): 33–36

    Article  Google Scholar 

  6. Singh V (2005). A novel global robust stability criterion for neural networks with delay. Phys Lett A 337: 369–373

    Article  ADS  Google Scholar 

  7. Liao XF and Yu JB (1998). Robust stability for interval Hopfield neural networks with time delay. IEEE Trans Neural Netw 9(5): 1042–1045

    Article  Google Scholar 

  8. Cao J, Huang D-S and Qu Y (2005). Global robust stability of delayed recurrent neural networks. Chaos, Solitons & Fractals 23(1): 221–229

    Article  MATH  Google Scholar 

  9. Arik S (2003). Global robust stability of delayed neural networks. IEEE Trans Circuits Syst I 50(1): 156–160

    Article  Google Scholar 

  10. Rong L (2005). LMI-based criteria for robust stability of Cohen-Grossberg neural networks with delay. Phys Lett A 339: 63–73

    Article  ADS  Google Scholar 

  11. Xu S, Lam J and Ho DWC (2005). Novel global robust stability criteria for interval neural networks with multiple time-varying delays. Phys Lett A 342: 322–330

    Article  ADS  Google Scholar 

  12. Singh V (2004). Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE Proc Control Theory Appl 151(1): 125–129

    Article  Google Scholar 

  13. Ye H and Michel AN (1996). Robust stability of nonlinear time-delay systems with applications to neural networks. IEEE Trans Circuits Syst I 43(7): 532–543

    Article  Google Scholar 

  14. Cao J and Wang J (2004). Delay-dependent robust stability of uncertain nonlinear systems with time delay. Appl Math Comput 154: 289–297

    Article  MATH  Google Scholar 

  15. Huang H, Cao J and Qu Y (2004). Global robust stability of delayed recurrent neural networks. J Comput Sys Sci 69: 688–700

    Article  MATH  Google Scholar 

  16. Chen A, Cao J and Huang L (2005). Global robust stability of interval cellular neural networks with time-varying delays. Chaos, Solitons & Fractals 23: 787–799

    Article  MATH  Google Scholar 

  17. Liao X and Wong K (2004). Robust stability of interval bidirectional associative memory neural network with time delays. IEEE Trans Syst Man Cyb 34(2): 1142–1154

    Article  Google Scholar 

  18. Yu W and Cao J (2007). Synchronization control of stochastic delayed neural networks. Physica A 373: 252–260

    Article  ADS  Google Scholar 

  19. Yu W (2007). A LMI-based approach to global asymptotic stability of neural networks with time varying delays. Nonlinear Dynam 48(1-2): 165–174 DOI: 10.1007/s11071-006-9080-6

    Article  Google Scholar 

  20. Yu W and Yao L (2007). Global robust stability of neural networks with time varying delays. J Comput Appl Math 206(2): 679–687 DOI: 10.1016/j.cam.2006.08.017

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  22. Liao X and Mao X (2000). Exponential stability of stochastic delay interval systems. Syst Contr Lett 40: 171–181

    Article  MATH  Google Scholar 

  23. Chen W, Guan Z and Liu X (2005). Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Sys Contr Lett 54: 547–555

    Article  MATH  Google Scholar 

  24. Wan L and Sun J (2005). Mean square exponential stability of stochastic delayed Hopfield neural networks. Phy Lett A 343: 306–318

    Article  ADS  Google Scholar 

  25. Yue D and Won S (2001). Delay-dependent robust stability of stochasitc systems with time delay and nonlinear uncertainties. IEE Electron Lett 37(15): 992–993

    Article  Google Scholar 

  26. Chen W, Xu J and Guan Z (2003). Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays. IEEE Trans Automa Contr 48(12): 2270–2276

    Article  Google Scholar 

  27. Wang Z, Ho DWC and Liu X (2005). State estimation for delayed neural networks. IEEE Trans Neural Netw 16(1): 279–284

    Article  Google Scholar 

  28. Moon Y, Park P, Kwon W and Lee Y (2001). Delay-dependent robust stabilization of uncertain state-delayed systems. Int J Contr 74(14): 1447–1455

    Article  MATH  Google Scholar 

  29. Wang Z, Goodall DP and Burnham KJ (2002). On designing observers for time-delay systems with non-linear disturbances. Int J Contr 75(11): 803–811

    Article  MATH  Google Scholar 

  30. Kolmanovskii VB and Myskis AD (1999). Introduction to the theory and applications of functional differential equations. Kluwer, Academic Publishers, Dordrecht

    MATH  Google Scholar 

  31. Schuss Z (1980) Theory and applications of stochastic differential equations, Wiley

  32. Cao J and Wang J (2005). Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I 52(2): 417–426

    Article  Google Scholar 

  33. Boyd S, Ghaoui LE, Feron E and Balakrishnan V (1994). Linear matrix inequalities in system and control theory. SIAM, Philadelphia, PA

    MATH  Google Scholar 

  34. Gu KQ, Kharitonov VL and Chen J (2003). Stability of time-delay systems. Birkhauser, Boston

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Wenwu Yu & Jinde Cao

  2. Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA

    Wenwu Yu

Authors
  1. Wenwu Yu
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  2. Jinde Cao
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Correspondence to Jinde Cao.

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Yu, W., Cao, J. Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay. Neural Process Lett 26, 101–119 (2007). https://doi.org/10.1007/s11063-007-9045-x

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  • DOI: https://doi.org/10.1007/s11063-007-9045-x

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