Skip to main content

LMI Approach for Stability of Cohen-Grossberg Neural Networks with Multi-delay and Distributed Delays

  • Conference paper
  • First Online:
Mechatronics and Automatic Control Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 237))

  • 1461 Accesses

Abstract

In this paper, stability of periodic solutions of the Cohen-Grossberg neural network with time delays and higher-order terms is investigated. Some sufficient conditions for global stability of periodic solutions are provided by employing Lyapunov-Krasovskii function and linear matrix inequality (LMI) approach. Simulation results show the feasibility and effectiveness of the proposed method.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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. Balasubramaniam P, Samath JA, Kumaresan N, Kumar VAA (2006) Solution of matrix Riccati differential equation for the linear quadratic singular system using neural networks. Appl Math Comput 182:1832–1839

    Article  MathSciNet  MATH  Google Scholar 

  2. Balasubramaniam P, Abdul Samath J, Kumaresan N (2007) Optimal control for nonlinear singular systems with quadratic performance using neural networks. Appl Math Comput 187:1535–1543

    Article  MathSciNet  MATH  Google Scholar 

  3. Cao J, Feng G, Wang Y (2008) Multistability and multiperiodicity of delayed Cohen–Grossberg neural networks with a general class of activation functions. Phys D 237:34–49

    Article  MathSciNet  Google Scholar 

  4. Xilin Fu, Xiaodi Li (2011) LMI conditions for stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays. Commun Nonlinear Sci Num Simul 16:435–454

    Article  MATH  Google Scholar 

  5. Cao J, Liang J (2004) Boundedness and stability for Cohen–Grossberg neural network with time-varying delays. J Math Anal Appl 296:665–685

    Article  MathSciNet  MATH  Google Scholar 

  6. Marcus C, Westervelt R (1989) Stability of analog neural networks with delay. Phys Rev A 39:347–359

    Article  MathSciNet  Google Scholar 

  7. Chen Wu, Dong Ruan (2006) Dynamics of some neural networks and the research on chaos theory (in Chinese). Ph.D. thesis, Fudan University, pp 46–47

    Google Scholar 

  8. Rakkiyappan R, Balasubramaniam P, Lakshmanan S (2008) Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. Phys Lett A 372:5290–5298

    Article  MathSciNet  MATH  Google Scholar 

  9. Jinde Cao (2007) Synchronization-based approach for parameters identification in delayed chaotic neural networks. Phys A Statis Mech Appl 382:672–682

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the reviewers and the editor for their helpful comments and constructive suggestions, and the authors Cao J, Xilin Fu,Wu chen et al.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Junfeng Cui .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Cui, J., Shao, H. (2014). LMI Approach for Stability of Cohen-Grossberg Neural Networks with Multi-delay and Distributed Delays. In: Wang, W. (eds) Mechatronics and Automatic Control Systems. Lecture Notes in Electrical Engineering, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-01273-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-01273-5_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01272-8

  • Online ISBN: 978-3-319-01273-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics