Skip to main content
SpringerLink
Log in

Stabilization of Stochastic RNNs with Stochastic Delays

  • Chapter
  • First Online:
Qualitative Analysis and Control of Complex Neural Networks with Delays

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 34))

  • 1155 Accesses

Abstract

The research in Chaps. 4–10 is focused on the qualitative analysis of complex neural networks with delays. It is well known that the qualitative analysis of nonlinear dynamical systems is the foundation of controlling the systems. Therefore, in this chapter controller design problem will be studied for a class of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time delays and Markovian switching, in which the neural dynamical networks will be stabilized. The contents in this chapter are from the research result in Zheng et al., (IEEE Trans. Neural Netw. Learn. Syst. 24(5):800–811, 2013, [1]).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. C. Zheng, Q. Shan, H. Zhang, Z. Wang, On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching. IEEE Trans. Neural Netw. Learn. Syst. 24(5), 800–811 (2013)

    Article  Google Scholar 

  2. Q. Song, Z. Wang, Neural networks with discrete and distributed time-varying delays: a general stability analysis. Chaos Solitons Fractals 37, 1538–1547 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. X.F. Liao, K. Wong, C.G. Li, Global exponential stability for a class of generalized neural networks with distributed delays. Nonlinear Anal. Real World Appl. 5, 527–547 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. C.H. Lien, L.Y. Chung, Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays. Chaos Solitons Fractals 34, 1213–1219 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Z. Liu, H. Zhang, Q. Zhang, Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional. IEEE Trans. Neural Netw. 21(11), 1710–1718 (2010)

    Article  Google Scholar 

  6. Z. Liu, S.C. Shih, Q. Wang, Global robust stabilizing control for a dynamic neural network system. IEEE Trans. Syst. Man Cybern. A 39(2), 426–436 (2009)

    Article  Google Scholar 

  7. F.O. Souza, L.A. Mozelli, R.M. Palhares, On stability and stabilization of T-S Fuzzy time-delayed systems. IEEE Trans. Fuzzy Syst. 17(6), 1450–1455 (2009)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. H. Zhang, T. Ma, G.B. Huang, Z. Wang, Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans. Syst. Man Cyber. B Cyber. 40(3), 831–844 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. J. Tian, Y. Li, J. Zhao, S. Zhong, Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates. Appl. Math. Comput. 218, 5769–5781 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  16. Z.G. Wu, J.H. Park, H. Su, J. Chu, Stochastic stability analysis of piecewise homogeneous Markovian jump neural networks with mixed time-delays. J. Frankl. Inst. 349, 2136–2150 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. S.M. Lee, O.M. Kwon, J.H. Park, A novel delay-dependent criterion for delayed neural networks of neutral type. Phys. Lett. A 374, 1843–1848 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. O.M. Kwon, S.M. Lee, J.H. Park, Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays. Phys. Lett. A 374, 1232–1241 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. R. Rakkiyappan, P. Balasubramaniam, Dynamic analysis of Markovian jumping impulsive stochastic Cohen-Grossberg neural networks with discrete interval and distributed time-varying delays. Nonlinear Anal.: Hybrid Syst. 3, 408–417 (2009)

    MathSciNet  MATH  Google Scholar 

  20. P. Balasubramaniam, R. Rakkiyappan, Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen-Grossberg neural networks with discrete interval and distributed time-varying delays. Nonlinear Anal.: Hybrid Syst. 3, 207–214 (2009)

    MathSciNet  MATH  Google Scholar 

  21. C. Vidhya, P. Balasubramaniam, 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, 181–196 (2011)

    MathSciNet  MATH  Google Scholar 

  22. C. Hua, X. Guan, Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks. IEEE Trans. Neural Netw. 19(4), 673–688 (2008)

    Article  MathSciNet  Google Scholar 

  23. V.N. Phat, New stabilization criteria for linear time-varying systems with state delay and norm-bounded uncertainties. IEEE Trans. Autom. Control 47(12), 2095–2098 (2002)

    Article  MathSciNet  Google Scholar 

  24. Z. Wang, Y. Liu, X. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans. Autom. Control 55(7), 1656–1662 (2010)

    Article  Google Scholar 

  25. E. Fridman, Descriptor discretized Lyapunov functional method: analysis and design. IEEE Trans. Autom. Control 51(5), 890–897 (2006)

    Article  MathSciNet  Google Scholar 

  26. X. Liu, Q. Wang, Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays. IEEE Trans. Neural Netw. 19(1), 71–79 (2008)

    Article  Google Scholar 

  27. V.N. Phat, H. Trinh, Exponential stabilization of neural networks with various activation functions and mixed time-varying delays. IEEE Trans. Neural Netw. 21(7), 1180–1184 (2010)

    Article  Google Scholar 

  28. J. Cao, S. Zhong, Y. Hu, Global stability analysis for a class of neural networks with varying delays and control input. Appl. Math. Comput. 189(2), 1480–1490 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. K. Patan, Stability analysis and the stabilization of a class of discrete-time dynamic neural networks. IEEE Trans. Neural Netw. 18(3), 660–673 (2007)

    Article  Google Scholar 

  30. M. Liu, Delayed standard neural network models for control systems. IEEE Trans. Neural Netw. 18(4), 1376–1391 (2007)

    Article  Google Scholar 

  31. J. Lu, D.W.C. Ho, Z. Wang, Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers. IEEE Trans. Neural Netw. 20(10), 1617–1629 (2009)

    Article  Google Scholar 

  32. E.N. Sanchez, J.P. Perez, Input-to-state stabilization of dynamic neural networks. IEEE Trans. Syst. Man Cybern. A 33(4), 532–536 (2003)

    Article  Google Scholar 

  33. Z. Chen, D. Zhao, Stabilization effect of diffusion in delayed neural networks systems with Dirichlet boundary conditions. J. Frankl. Inst. 348(10), 2884–2897 (2011)

    Article  MATH  Google Scholar 

  34. X. Lou, B. Cui, On robust stabilization of a class of neural networks with time-varying delays, in Proceedings of IEEE International Conference on Computational Intelligence and Security, pp. 437–440 (2006)

    Google Scholar 

  35. K. Shi, H. Zhu, S. Zhong et al., Less conservative stability criteria for neural networks with discrete and distributed delays using a delay-partitioning approach. Neurocomputing 140, 273–282 (2014)

    Article  Google Scholar 

  36. B. Chen, J. Wang, Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays. Neural Netw. 20(10), 1067–1080 (2007)

    Article  MATH  Google Scholar 

  37. Z. Guo, L. Huang, LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations. Appl. Math. Comput. 215, 889–900 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. H. Wu, Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations. Nonlinear Anal.: Real World Appl. 10, 2297–2306 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. K. Gu, An integral inequality in the stability problem of time-delay systems, in Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805–2810 (2000)

    Google Scholar 

  40. C. Zheng, Q.H. Shan, Z. Wang, Improved stability results for stochastic Cohen-Grossberg neural networks with discrete and distributed delays. Neural Process. Lett. 35(2), 103–129 (2012)

    Article  Google Scholar 

  41. L. Arnold, Stochastic Differential Equations: Theory and Applications (Wiley, New York, 1972)

    Google Scholar 

  42. X. Mao, Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans. Autom. Control 47(10), 1604–1612 (2002)

    Article  Google Scholar 

  43. C. Yuan, J. Lygeros, Stabilization of a class of stochastic differential equations with Markovian switching. Syst. Control Lett. 54, 819–833 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  44. B. Øksendal, Stochastic Differential Equations: An Introduction with Applications (Springer, New York, 1985)

    Book  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, China

    Zhanshan Wang & Zhenwei Liu

  2. Department of Mathematics, Dalian Jiaotong University, Dalian, China

    Chengde Zheng

Authors
  1. Zhanshan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenwei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chengde Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhanshan Wang .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Science Press, Beijing and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Wang, Z., Liu, Z., Zheng, C. (2016). Stabilization of Stochastic RNNs with Stochastic Delays. In: Qualitative Analysis and Control of Complex Neural Networks with Delays. Studies in Systems, Decision and Control, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47484-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-47484-6_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47483-9

  • Online ISBN: 978-3-662-47484-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation