Skip to main content
SpringerLink
Log in

Delay-Dependent and Delay-Independent Stability Conditions of Delayed Cellular Neural Networks

  • Conference paper
Neural Information Processing (ICONIP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4232))

Included in the following conference series:

  • 1437 Accesses

Abstract

By using the saturation linearity of the output functions of neurons in cellular neural networks, and by adopting the method of decomposing the state space to sub-regions, the mathematical equations of delayed cellular neural networks are rewritten to be the form of linear differential difference equations in the neighbourhood of each equilibrium, which is an interior point of some sub-region. Based on this linear form and by using the stability theory of linear differential difference equations and the tool of M-matrix, delay-dependent and delay-independent stability algebraic criteria are obtained. All results obtained in this paper need only to compute the eigenvalues of some matrices or to examine the matrices to be M-matrix or to verify some inequalities to be holden.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chua, L., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. Circuits and Systems 35, 1257–1272 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Slavova, A.: Stability Analysis of Cellular Neural Networks with Nonlinear Dynamics. Nonlinear Analysis: Real World Applications 2, 93–103 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Liao, W., Liao, X.: Stability Analysis of Cellular Neural Networks. Control Theroy and Applications 20(1), 89–92 (2003)

    Google Scholar 

  4. Civalleri, P., Gill, M., Pandolfli, L.: On Stability of Cellular Neural Networks with Delay. IEEE Trans. Circuits and Systems 40(3), 157–165 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cao, J., Zhou, D.: Stability Analysis of Delayed Celluar Neural Networks. Neural Networks 11, 1601–1605 (1998)

    Article  Google Scholar 

  6. Takahashi, N.: A New Sufficient Condition for Complete Stability of Cellular Neural Networks with Delay. IEEE Trans. Circuits and Systems-1: Fundamental Theory and Applications 47(6), 793–799 (2000)

    Article  Google Scholar 

  7. Liao, T., Wang, F.: Global Stability for Cellular Neural Networks with Time Delay. IEEE Trans. Neural Networks 11(6), 1481–1484 (2000)

    Article  Google Scholar 

  8. Liao, X.: Mathematical Theory of Cellular Neural Networks 1. China Science 24(9), 902–910 (1994)

    Google Scholar 

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

    MATH  Google Scholar 

  10. Qin, Y., Liu, Y., Wang, L.: Motion Stability of Dynamical Systems with Time- Delays, 2nd edn. Science Press, Beijing (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zhongyuan University of Technology, Zhengzhou Henan, 450007, China

    Wudai Liao, Dongyun Wang & Yulin Xu

  2. Huazhong University of Science and Technology, Wuhan Hubei, 430074, China

    Xiaoxin Liao

Authors
  1. Wudai Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongyun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yulin Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaoxin Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, The Chinese Univ. of Hong Kong, Shatin, N.T., Hong Kong

    Irwin King

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  3. The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Lai-Wan Chan

  4. Department of Computer Science and Engineering & Center for Cognitive Science, The Ohio State University, OH 43210, Columbus

    DeLiang Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liao, W., Wang, D., Xu, Y., Liao, X. (2006). Delay-Dependent and Delay-Independent Stability Conditions of Delayed Cellular Neural Networks. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893028_59

Download citation

  • DOI: https://doi.org/10.1007/11893028_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46479-2

  • Online ISBN: 978-3-540-46480-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation