Skip to main content
SpringerLink
Log in
Book cover

Qualitative Analysis and Control of Complex Neural Networks with Delays pp 173–204Cite as

Delay-Partitioning-Method Based Stability Results for RNNs

  • Chapter
  • First Online:

  • 1158 Accesses

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

Abstract

Chapter 3 has presented many ways on how to use the time delay to establish the effective stability criteria for RNNs with delays. In this chapter, inspired by the discussion in Chap. 3, a new delay splitting method is proposed. By nonuniformly splitting the interval of time delay through involving many adjustable parameters, along with the construction of a new Lyapunov function, some delay-dependent stability results are established. By some comments and comparisons with the existing results, the effectiveness and novelty of the obtained criteria are verified.

This is a preview of subscription content, 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

Learn about institutional subscriptions

References

  1. L.O. Chua, L. Yang, Cellular neural networks: applications. IEEE Trans. Circuits Syst. 35(10), 1273–1290 (1988)

    Article  MathSciNet  Google Scholar 

  2. T. Roska, L.O. Chua, Cellular neural networks with non-linear and delay-type template elements and non-uniform grids. Int. J. Circuit Theory Appl. 20(5), 469–481 (1992)

    Article  MATH  Google Scholar 

  3. Y.H. Chen, S.C. Fang, Neurocomputing with time delay analysis for solving convex quadratic programming problems. IEEE Trans. Neural Netw. 11(1), 230–240 (2000)

    Article  Google Scholar 

  4. Y. Xia, J. Wang, A general projection neural network for solving monotone variational inequalities and related optimization problems. IEEE Trans. Neural Netw. 15(2), 318–328 (2004)

    Article  MathSciNet  Google Scholar 

  5. R. Fantacci, M. Forti, M. Marini, L. Pancani, Cellular neural networks approach to a class of communication problems. IEEE Trans. Circuits Syst. I, Fund. Theory Appl. 46(12), 1457–1467 (1999)

    Article  Google Scholar 

  6. J.A. Farrell, A.N. Michel, A synthesis procedure for Hopfield’s continuous-time associative memory. IEEE Trans. Circuits Syst. 37(7), 877–884 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. A.N. Michel, J.A. Farrell, H.F. Sun, Analysis and synthesis techniques for Hopfield type synchronous discrete-time neural networks with applications to associative memory. IEEE Trans. Circuits Syst. 37(11), 1356–1366 (1990)

    Article  MathSciNet  Google Scholar 

  8. T. Nishikawa, Y.C. Lai, F.C. Hoppensteadt, Capacity of oscillatory associative-memory networks with error-free retrieval. Phys. Rev. Lett. 92(10), 101–108 (2004)

    Article  Google Scholar 

  9. D.L. Wang, Emergent synchrony in locally coupled neural oscillators. IEEE Trans. Neural Netw. 6(4), 941–948 (1995)

    Article  Google Scholar 

  10. S.S. Young, P.D. Scott, N.M. Nasrabadi, Object recognition using multilayer Hopfield neural network. IEEE Trans. Image Process. 6(3), 357–372 (1997)

    Article  Google Scholar 

  11. T. Liao, F. Wang, Global stability for cellular neural networks with time delay. IEEE Trans. Neural Netw. 11(6), 1481–1484 (2000)

    Article  Google Scholar 

  12. S. Arik, An analysis of global asymptotic stability of delayed neural networks. IEEE Trans. Neural Netw. 13(5), 1239–1242 (2002)

    Article  Google Scholar 

  13. S. Arik, Global aymptotic stability of a larger class of neural networks with constant time delay. Phys. Lett. A 311, 504–511 (2003)

    Article  MATH  Google Scholar 

  14. V. Singh, A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Netw. 15(1), 223–225 (2004)

    Article  Google Scholar 

  15. J. Cao, J. Wang, Global asymptotic stability of a class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. I 50(1), 34–44 (2003)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  17. J. Cao, J. Wang, Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 52(5), 920–931 (2005)

    Article  MathSciNet  Google Scholar 

  18. 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 

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

    Article  Google Scholar 

  20. X. Liao, G. Chen, E. Sanchez, Delay-dependent exponential stability analysis of delay neural networks: An LMI approch. Neural Netw. 15, 855–866 (2002)

    Article  Google Scholar 

  21. S. Xu, J. Lam, D. Wu, Y. Zou, New global asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Circuits Syst. II, Exp. Br. 52(6), 349–353 (2005)

    Article  Google Scholar 

  22. C. Hua, C. Long, X. Guan, New results on stability analysis of neural networks with time-varying delays. Phys. Lett. A 352, 335–340 (2006)

    Article  MATH  Google Scholar 

  23. H. Cho, J. Park, Novel delay-dependent robust stability criterion of delayed cellular neural networks. Chaos Solitons Fractals 32, 1194–1200 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Sathy, P. Balasubramaniam, R. Chandran, Robust stability of fuzzy Markov type Cohen-Grossberg neural networks by delay decomposition approach. Iranian J. Fuzzy Syst. 11(2), 1–16 (2014)

    MathSciNet  Google Scholar 

  25. X. Zhou, J. Tian, H. Ma, Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays. Neurocomputing 129, 401–408 (2014)

    Article  Google Scholar 

  26. X. Liao, Y. Liu, H. Wang, Exponential estimates and exponential stability for neutral-type neural networks with multiple delays. Neurocomputing 14, 868–883 (2015)

    Article  Google Scholar 

  27. W. Feng, S. Yang, H. Wu, Further results on robust stability of bidirectional associative memory neural networks with norm-bounded uncertainties. Neurocomputing 148, 535–543 (2015)

    Article  Google Scholar 

  28. H. Zhang, Z. Liu, G. 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 

  29. Y. He, M. Wu, J. She, Delay-dependent exponential stability of delayed neural networks with time-varying delay. IEEE Trans. Circuits Syst. II, Exp. Br. 53(7), 553–557 (2006)

    Article  Google Scholar 

  30. Y. He, G. Liu, D. Rees, New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans. Neural Netw. 18(1), 310–314 (2007)

    Article  MathSciNet  Google Scholar 

  31. Y. He, G. Liu, D. Rees, M. Wu, Stability Analysis for neural networks with time-varying interval delay. IEEE Trans. Neural Netw. 18(6), 1850–1854 (2007)

    Article  Google Scholar 

  32. M. Parlakçi, Robust stability of uncertain neutral systems: a novel augmented Lyapunov functional approach. IET Control Theory Appl. 1(3), 802–809 (2007)

    Article  MathSciNet  Google Scholar 

  33. C. Peng, Y. Tian, Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. J. Comput. Appl. Math. 214(2), 480–494 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  34. T. Li, L. Guo, C. Sun, C. Lin, Further result on delay-dependent stability criterion of neural networks with time-varying delays. IEEE Trans. Neural Netw. 19(4), 726–730 (2008)

    Article  Google Scholar 

  35. X.G. Li, X.J. Zhu, Stability analysis of neutral systems with distributed delays. Automatica 44(8), 2197–2201 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. E. Fridman, U. Shaked, A descriptor system approach to \(H_{\infty }\) control of linear time-delay systems. IEEE Trans. Autom. Control 47(2), 253–270 (2002)

    Article  MathSciNet  Google Scholar 

  37. S. Mou, H. Gao, J. Lam, W. Qiang, A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay. IEEE Trans. Neural Netw. 19(3), 532–535 (2008)

    Article  Google Scholar 

  38. K. Gu, V. Kharitonov, J. Chen, Stability of Time-Delay Systems, (Cambridge University Press, Cambridge, 2003)

    Google Scholar 

  39. M. Liu, Delayed standard neural network model and its application. ACTA Automatica Sinica 31(5), 750–758 (2005). (in Chinese)

    Google Scholar 

  40. J. Hale, Theory of Functional Differential Equations (Springer, New York, 1977)

    Book  MATH  Google Scholar 

  41. J.A. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 7, 308–313 (1965)

    Article  MATH  Google Scholar 

  42. P. Park, J. Ko, Stability and robust stability for systems with a time-varying delay. Automatica 43(10), 1855–1858 (2007)

    Article  MathSciNet  MATH  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). Delay-Partitioning-Method Based Stability Results for RNNs. 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_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-47484-6_4

  • 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