New results for global stability of neutral-type delayed neural networks

  • Neyir Ozcan 
  • Department of Electrical and Electronics Engineering Faculty of Engineering, Uludag University, Bursa, Turkey
Cite as
Ozcan N. (2018). New results for global stability of neutral-type delayed neural networks. Proceedings of the 11th International Conference on Integrated Modeling and Analysis in Applied Control and Automation (IMAACA 2018), pp. 28-33. DOI: https://doi.org/10.46354/i3m.2018.imaaca.004

Abstract

"This paper deals with the stability analysis of the class of
neutral-type neural networks with constant time delay.
By using a suitable Lyapunov functional, some delay
independent sufficient conditions are derived, which
ensure the global asymptotic stability of the equilibrium
point for this this class of neutral-type neural networks
with time delays with respect to the Lipschitz activation
functions. The presented stability results rely on
checking some certain properties of matrices. Therefore,
it is easy to verify the validation of the constraint
conditions on the network parameters of neural system
by simply using some basic information of the matrix
theory."

References

  1. Alsaadi F. E., Luo Y., Liu Y. and Wang Z., 2018. State estimation for delayed neural networks with stochastic communication protocol: The finite-time case. Neurocomputing, 281, 86-95.
  2. Aouiti C., Gharbia I. B., Cao J., MhamdiM. S. And Alsaedi A., 2018. Existence and global exponential stability of pseudo almost periodic solution for neutraldelay BAM neural networks with timevarying delay in leakage terms. Chaos, Solitons and Fractals, 107, 111-127.
  3. Chen J., Chen B. and Zeng Z., 2018. Global uniform asymptotic fixed deviation stability and stability for delayed fractional-order memristive neural networks with generic memductance. Neural Networks, 98, 65-75.
  4. Cheng C.J., Liao T. L., Yan J.J. and Hwang C. C., 2016. Globally asymptotic stability of a class of neutraltype neural networks with delays. IEEE Transactions on Systems Man and Cybernetics- Part B, 6 (5), 1191-1195.
  5. Chua L. O. and Yang L., 1988. Cellular Neural Networks: Theory. IEEE Transactions on Circuits and Syststems-I, 35 (10), 1257-1272.
  6. Cohen M. and Grossberg S., 1983. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions Systems,Man and Cybernetics, 13 (5), 815-826.
  7. Hopfield J. J., 1982. Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci., 79 (8), 2554-2558.
  8. Huang H., Du Q. and Kang X., 2013. Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters  and mixed time delays. ISA Transactions, 52, 759-767.
  9. Kwon O.M. and Park J. H., 2008. New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays. Applied Mathematics and Computation, 205, 417-427.
  10. Li S. and Xu D., 2011. Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays. Nonlinear Dynamics, 64, 65-75.
  11. Li X. and Cao J., 2010. Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity, 23, 1709-1726.
  12. Liu L., 2017. New criteria on exponential stability for stochastic delay differential systems based on vector Lyapunov function. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (11), 2985-2993.
  13. Lou X. and Cui B., 2009. Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters. Chaos, Solitons and Fractals, 39, 2188-2197.
  14. Lv Y., Lv W. and Sun J., 2008. Convergence Dynamics of stochastic reactiondiffusion recurrent neural networks with continuously distributed delays. Nonlinear Analysis: Real World Applications, 9 (4), 1590-1606.
  15. Mohamad S. and Gopalsamy K., 2003. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Applied Mathematics and Computation, 135 (1), 17-38.
  16. Park J. H. and Kwon O.M., 2008. Design of state estimator for neural networks of neutral-type. Applied Mathematics and Computation, 202, 360- 369.
  17. Rajchakit G., Saravanakumar R., Ahn C. K. and Karimi H. R., 2017. Improved exponential convergence result for generalized neural networks including interval time- varying delayed signals. Neural Networks, 86, 10-17.
  18. Rakkiyappan R., Maheswari K. and Sivaranjani K., 2017. Non-weighted H-infinity state estimation for discrete-time switched neural networks with persistent dwell time switching regularities based on Finslers lemma. Neurocomputing, 260, 131-141.
  19. Samidurai R., Rajavel S., Sriraman R., Cao J., Alsaedi A. and Alsaadi F. E., 2017. Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay. International Journal of Control, Automation and Systems, 15 (4), 1888-1900.
  20. Samli R. and Arik S., 2009. New results for global stability of a class of neutral-type neural systems with time delays. Applied Mathematics and Computation, 210, 564-570.
  21. Shen Y. and Wang J., 2008. An improved algebraic criterion for global exponential stability of
    recurrent neural networks with time-varying delays. IEEE Transactions on Neural Networks, 19 (3), 528-531.
  22. Shi K., Zhu H., Zhong S., Zeng Y. and Zhang Y., 2015. New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach. Journal of the Franklin Institute, 352, 155-176.
  23. Song Q., Yu Q., Zhao Z., Liu Y. and Alsaadi F. E., 2018. Dynamics of complex-valued neural networks with variable coefficients and proportional delays. Neurocomputing, 275, 2762-2768.
  24. Wang B., Yan J., Cheng J. and Zhong S., 2017. New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals. Applied Mathematics and Computation, 314, 322-333.
  25. Wang J., Jiang H., Ma T. and C. Hu, 2018. Delaydependent dynamical analysis of complex-valued memristive neural networks: Continuous-time and discrete-time cases. Neural Networks, 101, 33-46.
  26. Wang L. and Zou X., 2002. Exponentially stability of Cohen-Grossberg neural networks. Neural Networks, 15 (3), 415-422.
  27. Yang B. and Wang J., 2017. Stability analysis of delayed neural networks via a new integral inequality. Neural Networks, 88, 49-57.
  28. Yang W., Yu W., Cao J., Alsaadi F. E. and Hayat T., 2018. Global exponential stability and lag
    synchronization for delayed memristive fuzzy CohenGrossberg BAM neural networks with
    impulses. Neural Networks, 98, 122-153.
  29. Yen E. C., 2011. Solubility and stability of recurrent neural networks with nonlinearity or time-varying delays. Communications in Nonlinear Science and Numerical Simulation, 16 (1), 509-521.
  30. Zhang G., Wang T., Li T. and Fei S., 2018. Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks. Neurocomputing, 275, 1782-1792.
  31. Zheng M., Li L., Peng H., Xiao J., Yang Y. and Zhao H., 2017. Finite-time stability analysis for neutral-type neural networks with hybrid time-varying delays without using Lyapunov method. Neurocomputing, 238, 67-75.