Stochastic stability analysis for a neutral-type neural networks with Markovian jumping parameters

Volume 10, Issue 7, pp 3409--3418 http://dx.doi.org/10.22436/jnsa.010.07.05

Publication Date: July 21, 2017 Submission Date: May 29, 2017

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Authors

Song Guo - Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu, 223300, P. R. China. Bo Du - Department of Mathematics, Huaiyin Normal University, Huaian , Jiangsu, 223300, P. R. China.

Abstract

In this paper, the stability problem is studied for a class of stochastic neutral-type neural networks with Markovian jumping parameters. By using fixed point theorem, the existence and uniqueness of solution for the neural networks system are obtained. Furthermore, based on the Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the mean square stability of the neural networks. An example is given to show the effectiveness of the proposed stability criterion.

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Keywords

• Markovian jumping parameters
• linear matrix inequality
• mean square stability.

MSC

•  34B15

References

• [1] S. Arik, Global robust stability analysis of neural networks with discrete time delays, Chaos Solitons Fractals, 26 (2005), 1407–1414.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1994)
  • View Article
  • MathSciNet
  • Google Scholar


• [3] H.-W. Chen, Z.-M. He, J.-L. Li, Multiplicity of solutions for impulsive differential equation on the half-line via variational methods, Bound. Value Probl., 2016 (2016), 15 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] K. Gu, An integral inequality in the stability problem of time-delay systems, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney Australia, 3 (2000), 2805–2810.
  • View Article
  • Google Scholar


• [5] Z.-J. Gui, W.-G. Ge, X.-S. Yang, Periodic oscillation for a Hopfield neural networks with neutral delays, Phys. Lett. A, 364 (2007), 267–273.
  • View Article
  • Google Scholar
  • MATH


• [6] M. P. Kennedy, L. O. Chua, Neural networks for nonlinear programming, IEEE Trans. Circuits and Systems, 35 (1988), 554–562.
  • View Article
  • Google Scholar


• [7] Y.-R. Liu, Z.-D. Wang, X.-H. Liu, Exponential synchronization of complex networks with Markovian jump and mixed delays, Phys. Lett. A, 372 (2008), 3986–3998.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] Y.-R. Liu, Z.-D. Wang, X.-H. Liu, State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays, Phys. Lett. A, 372 (2008), 7147–7155.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] S.-S. Mou, H.-J. Gao, J. Lam, W.-Y. Qiang, A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay, IEEE Trans. Neural Netw., 19 (2008), 532–535.
  • View Article
  • Google Scholar


• [10] J. Pan, X.-Z. Liu, W. -C. Xie, Exponential stability of a class of complex-valued neural networks with time-varying delays, Neurocomputing, 164 (2015), 293–299.
  • View Article
  • Google Scholar


• [11] J. H. Park, C. H. Park, O. M. Kwon, S. M. Lee, A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput., 199 (2008), 716–722.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] R. Rakkiyappan, P. Balasubramaniam, J.-D. Cao, Global exponential stability results for neutral-type impulsive neural networks, Nonlinear Anal. Real World Appl., 11 (2010), 122–130.
  • View Article
  • MathSciNet
  • Google Scholar


• [13] J. E. Slotine, W.-P. Li, Applied nonlinear control, Prentice-Hall, Englewood Cliffs, New Jersey (1991)
  • Google Scholar


• [14] Z.-D. Wang, Y.-R. Liu, X.-H. Liu, State estimation for jumping recurrent neural networks with discrete and distributed delays, Neural Netw., 22 (2009), 41–48.
  • View Article
  • Google Scholar
  • MATH


• [15] Z.-H. Xia, X.-H. Wang, X.-M. Sun, Q. Wang, A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data, IEEE Trans. Parallel Distrib. Syst., 27 (2015), 340–352.
  • View Article
  • Google Scholar


• [16] Y. Xu, Z.-M. He, Exponential stability of neutral stochastic delay differential equations with Markovian switching, Appl. Math. Lett., 52 (2016), 64–73.
  • View Article
  • MathSciNet
  • Google Scholar


• [17] K.-W. Yu, C.-H. Lien, Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos Solitons Fractals, 38 (2008), 650–657.
  • View Article
  • Google Scholar


• [18] J. Zhao, D. J. Hill, T. Liu, Global bounded synchronization of general dynamical networks with nonidentical nodes, IEEE Trans. Automat. Controll, 57 (2012), 2656–2662.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH