Skip to main content
SpringerLink
Log in

Lagrange Stability for Memristor-Based Neural Networks with Time-Varying Delay via Matrix Measure

  • Conference paper
  • First Online:
Advances in Neural Networks – ISNN 2015 (ISNN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9377))

Included in the following conference series:

  • 2369 Accesses

Abstract

In this paper, we study the global exponential stability in Lagrange sense for memristor-based neural networks (MBNNs) with time-varying delays. Based on the nonsmooth analysis and differential inclusion theory, matrix measure technique is employed to establish some succinct criteria which ensure the Lagrange stability of the considered memristive model. In addition, the new proposed criteria are very easy to verify, and they also enrich and improve the earlier publications. Finally, two example are given to demonstrate the validity of the results.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Wu, A., Zeng, Z.: Lagrange Stability of Memristive Neural Networks With Discrete and Distributed Delays. IEEE Transactions on Neural networks and Learning Systems 25, 690–703 (2014)

    Article  Google Scholar 

  2. Zhang, G., Shen, Y., Xu, C.: Global Exponential Stability in a Lagrange Sense for Memristive Recurrent Neural Networks With Time-Varying Delays. Neurocomputing 149, 1330–1336 (2015)

    Article  Google Scholar 

  3. Ding, S., Wang, Z.: Stochastic Exponential Synchronization Control of Memristive Neural Networks With Multiple Time-Varying Delays. Neurocomputing 162, 16–25 (2015)

    Article  Google Scholar 

  4. Wu, H., Li, R., Zhang, X., Yao, R.: Weak, Modified and Function Projective Synchronization of Chaotic Memristive Neural Networks With Time Delays. Neurocomputing 149, 667–676 (2015)

    Article  Google Scholar 

  5. Guo, Z., Wang, J., Yang, Z.: Attractivity Analysis of Memristor-Based Cellular Neural Networks With Time-Varying Delays. IEEE Transactions on Neural Networks and Learning Systems 25, 704–717 (2014)

    Article  Google Scholar 

  6. Qi, J., Li, C., Huang, T.: Stability of Delayed Memristive Neural Networks With Time-Varying Impulses. Cogn. Neurodyn. 8, 429–436 (2014)

    Article  Google Scholar 

  7. Zhang, G., Shen, Y.: New Algebraic Criteria for Synchronization Stability of Chaotic Memristive Neural Networks With Time-Varying Delays. IEEE Transactions on Neural networks and Learning Systems 24, 1701–1707 (2013)

    Article  Google Scholar 

  8. Wen, S., Zeng, Z., Huang, T.: Adaptive Synchronization of Memristor-Based Chua’s Circuits. Physics Letters A 376, 2775–2780 (2012)

    Article  MATH  Google Scholar 

  9. Chen, J., Zeng, Z., Jiang, P.: On the Periodic Dynamics of a Memristor-Based Neural Networks With Time-Varying Delays. Information Science 279, 358–373 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, Z., Zhang, H., Jiang, B.: LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures. IEEE Transactions on Neural Networks and Learning Systems 22, 1032–1045 (2011)

    Article  Google Scholar 

  11. Wang, Z., Liu, L., Shan, Q., Zhang, H.: Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE Transactions on Neural Networks and Learning Systems (2015). doi:10.1109/TNNLS.2014.2387434

    Google Scholar 

  12. Liao, X., Luo, Q., Zeng, Z., Guo, Y.: Global Exponential Stability in Lagrange Sense for Recurrent Neural Networks With Time Delays. Nonlinear Analysis: Real World Applications 9, 1535–1557 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Luo, Q., Zeng, Z., Liao, X.: Global Exponential Stability in Lagrange Sense for Neutral Type Recurrent Neural Networks. Neurocomputing 74, 638–645 (2011)

    Article  Google Scholar 

  14. Vidyasagar, M.: Nonlinear System Analysis. Prentice-Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  15. Zhang, S., Xia, Y., Zheng, W.: A complex-valued neural dynamical optimization approach and its stability analysis. Neural Networks 61, 59–67 (2015)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Sanbo Ding & Zhanshan Wang

  2. Liaoning Province Product Quality Supervision Procuratorate, Shenyang, 110004, China

    Linlin Zhao

Authors
  1. Sanbo Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linlin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhanshan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanbo Ding .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, China

    Xiaolin Hu

  2. Fuzhou University, Fuzhou, China

    Yousheng Xia

  3. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China

    Yunong Zhang

  4. Chinese Academy of Sciences, Institute of Automation, Beijing, China

    Dongbin Zhao

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Ding, S., Zhao, L., Wang, Z. (2015). Lagrange Stability for Memristor-Based Neural Networks with Time-Varying Delay via Matrix Measure. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25393-0_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25392-3

  • Online ISBN: 978-3-319-25393-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation