Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

New stability criteria for Cohen–Grossberg neural networks with time delays

New stability criteria for Cohen–Grossberg neural networks with time delays

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Add to cart
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)
Add to cart

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

  • Author(s): L. Hu 1 ; H. Gao 1 ; P. Shi 2, 3
    • View affiliations
    • Affiliations: 1: Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, People's Republic of China
      2: Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd, UK
      3: School of Engineering and Science, Victoria University, Melbourne, Australia
  • Source: Volume 3, Issue 9, September 2009, p. 1275 – 1282
    DOI:  10.1049/iet-cta.2008.0213 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

The asymptotic stability is investigated for a class of time-delay Cohen–Grossberg neural networks, either with or without parameter uncertainties. By introducing a novel Lyapunov functional with the ideal of delay fractioning, a new criterion of asymptotic stability is derived in terms of a linear matrix inequality (LMI), which can be efficiently solved via standard numerical software. The criterion proves to be less conservative and the conservatism could be notably reduced by thinning the delay fractioning. Two examples are provided to demonstrate the less conservatism and effectiveness of the proposed stability conditions.

Inspec keywords: uncertain systems; delays; Lyapunov methods; asymptotic stability; linear matrix inequalities; neurocontrollers

Other keywords: linear matrix inequality; Lyapunov function; asymptotic stability; parameter uncertain system; Cohen-Grossberg neural network; time delay

Subjects: Distributed parameter control systems; Linear algebra (numerical analysis); Neurocontrol; Stability in control theory

References

    1. 1)
      • S. Grossberg . Nonlinear neural networks: principles, mechanisms, and architectures. Neural Netw. , 1 , 17 - 61
    2. 2)
      • H. Gao , T. Chen . New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control. , 2 , 553 - 557
    3. 3)
      • Y. Chen , W. Su . New robust stability of cellular neural networks with time-varying discrete and distributed delays. Int. J. Innov. Comput. Inf. Control , 1549 - 1556
    4. 4)
      • Z. Wang , D.W.C. Ho , X. Liu . State estimation for delayed neural networks. IEEE Trans. Neural. Netw. , 1 , 279 - 284
    5. 5)
      • Y. Chen , W. Su . New robust stability of cellular neural networks with time-varying discrete and distributed delays. Phys. Lett. A , 6 , 1549 - 1556
    6. 6)
      • S. Mou , H. Gao , W. Qiang , K. Chen . New delay-dependent exponential stability for neural networks with time delay. IEEE Trans. Systems Man Cybern. B , 2 , 571 - 576
    7. 7)
      • W. Wu , B.T. Cui , X.Y. Lou . Some criteria for asymptotic stability of Cohen–Grossberg neural networks with time-varying delays. Neurocomputing , 1085 - 1088
    8. 8)
      • S. Xu , J. Lam , D.W.C. Ho . A new LMI condition for delay-dependent asymptotic stability of delayed Hopfield neural networks. IEEE Trans. Circuits Syst. (II) , 3 , 230 - 234
    9. 9)
      • J. Cao , J. Liang . Boundedness and stability for Cohen–Grossberg neural network with time-varying delays. Math. Anal. Appl. , 2 , 665 - 685
    10. 10)
      • W. Lu , T. Chen . New conditions on global stability of Cohen–Grossberg neural networks. Neural Comput. , 5 , 1173 - 1189
    11. 11)
      • T. Li , S. Fei . Stability analysis on Cohen–Grossberg neural networks with both time-varying and distributed delays. Neurocomputing , 1069 - 1081
    12. 12)
      • Z. Wang , F. Yang , D.W.C. Ho , X. Liu . Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Physica A , 4 , 288 - 297
    13. 13)
      • Z. Mao , H. Zhao , X. Wang . Dynamics of Cohen–Grossberg neural networks with variable and distributed delays. Physica D , 1 , 11 - 22
    14. 14)
      • Y. He , M. Wu , J.H. She . An improved global asympotic stability criterion for delayed cellular neural networks. IEEE Trans. Neural. Netw. , 1 , 250 - 252
    15. 15)
      • B. Cui , W. Wu . Global exponential stability of Cohen–Grossberg neural networks with distributed delays. Neurocomputing , 386 - 391
    16. 16)
      • M.A. Cohen , B. Grossberg . Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. , 5 , 815 - 826
    17. 17)
      • W. Wang , J. Cao . LMI-based criteria for globally robust stability of delayed Cohen–Grossberg neural networks. IEE Proc. Control Theory Appl. , 4 , 397 - 402
    18. 18)
      • H. Gao , J. Lam , G. Chen . New criteria for synchronization stability of general complex dynamical networks with coupling delays. Physica A , 2 , 263 - 273
    19. 19)
      • M.P. Kennedy , L.O. Chua . Neural networks for nonlinear programming. IEEE Trans. Circuits Syst. , 5 , 554 - 562
    20. 20)
      • L. Wu , P. Shi , H. Gao , C. Wang . Delay-dependent robust H∞ and H2−H∞ filtering for LPV systems with both discrete and distributed delays. IET Control Theory Appl. , 4 , 483 - 492
    21. 21)
      • S. Mou , H. Gao , J. Lam . A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delays. IEEE Trans. Neural Netw. , 3 , 532 - 535
    22. 22)
      • X.F. Liao , S.T. Guo . Delay-dependent asymptotic stability of Cohen–Grossberg models with multiple time-varying delays. Discret. Dyn. Nat. Soc. , 1 - 17
    23. 23)
      • S. Boyd , L.E. Ghaoui , E. Feron , V. Balakrishnan . (1994) Linear matrix inequalities in system and control theory.
    24. 24)
      • X.M. Sun , J. Zhao , W. Wang . Two design schemes for robust adaptive control of a class of linear uncertain neutral delay systems. Int. J. Innov. Comput. Inf. Control , 2 , 385 - 396
    25. 25)
      • R. Wang , J. Zhao . Exponential stability analysis for discrete-time switched linear systems with time-delay. Int. J. Innov. Comput. Inf. Control , 1557 - 1564
    26. 26)
      • X.F. Liao , C.G. Li , K.W. Wong . Criteria for exponential stability of Cohen–Grossberg neural networks. Neural Netw. , 10 , 1401 - 1414
    27. 27)
      • Y. Takahashi . Solving optimization problems with variable-constraint by extended Cohen–Grossberg model. IEEE Trans. Syst. Man Cybern: A , 6 , 771 - 800
    28. 28)
      • T. Li , S. Fei , Y. Guo , Q. Zhu . Dynamics of Cohen–Grossberg neural networks with variable and distributed delays. Nonlinear Anal. Real World Appl. , 1 , 2600 - 2612
    29. 29)
      • H. Ye , A.N. Michel , K. Wang . Qualitative analysis of Cohen–Grossberg neural networks with multiple delays. Phys. Rev. E. , 3 , 2611 - 2618
    30. 30)
      • Z. Zuo , y. Wang . Robust stability criterion for delayed cellular neural networks with norm-bounded uncertainties. IEE Proc. Control Theory Appl. , 1 , 387 - 392
    31. 31)
      • Z. Wang , Y. Liu . On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A , 299 - 308
    32. 32)
      • L. Rong . LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay. Physics Lett. A. , 63 - 73
    33. 33)
      • J. Cao , D.W.C. Ho . A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach. Chaos Solitons Fractals , 5 , 1317 - 1329
    34. 34)
      • P. Shi , E.K. Boukas , R.K. Agarwal . Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay. IEEE Trans. Autom. Control. , 11 , 2139 - 2144
    35. 35)
      • Z. Chen , D. Zhao , J. Ruan . Dynamic analysis of high-order Cohen–Grossberg neural networks with time delay. Chaos Solitons Fractals , 4 , 1538 - 1546
    36. 36)
      • L.O. Chua , T. Roska . (1992) CNN: a new paradigm of nonlinear dynamics in space.
    37. 37)
      • Y. Li . Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays. Chaos Solitons Fractals , 3 , 459 - 466
    38. 38)
      • Y. Meng , S. Guo , L. Huang . Convergence dynamics of Cohen–Grossberg neural networks with continuously distributed delays. Appl. Math. Comput. , 1 , 188 - 199
    39. 39)
      • Y. He , M. Wu , J.H. She . Delay-dependent exponential stability of delayed neural networks with time-varying delay. IEEE Trans. Circuits Syst. (II) , 7 , 553 - 557
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2008.0213
Loading

Related content

content/journals/10.1049/iet-cta.2008.0213
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address