Abstract
In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Cao, J.: On stability of delayed cellular neural networks. Phys. Lett. A 261, 303–308 (1999)
Cao, J., Wang, J.: Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circ. Syst. I 50, 34–44 (2003)
Liang, J., Cao, J.: Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays. Phys. Lett. A 314, 434–442 (2003)
Arik, S.: An analysis of exponential stability of delayed neural networks with time varying delays. Neural Netw. 17, 1027–1031 (2004)
Xu, S., Lam, J., Ho, D.W.C.: Novel global asymptotical stability criteria for delayed cellular neural networks. IEEE Trans. Circ. Syst. II 52, 349–353 (2005)
Cao, J., Yuan, K., Li, H.X.: Global asymptotical stability of generalized recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Netw. 17(6), 1646–1651 (2006)
Haykin, S.: Neural Networks. Prentice Hall, New York (1994)
Liao, X., Mao, X.: Exponential stability and instability of stochastic neural networks. Stoch. Anal. Appl. 14, 165–185 (1996)
Mao, X.: Exponential Stability of Stochastic Differential Equations. Marcel Dekker, New York (1994)
Blythe, S., Mao, X., Liao, X.: Stability of stochastic delay neural networks. J. Franklin Inst. 338, 481–495 (2001)
Wan, L., Sun, J.: Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A 343, 306–318 (2005)
Zhao, H., Ding, N.: Dynamic analysis of stochastic Cohen–Grossberg neural networks with time delays. Appl. Math. Comput. 183, 464–470 (2006)
Wang, Z., Lauria, S., Fang, J., Liu, X.: Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos Solitons Fractals 32, 62–72 (2007)
Sun, Y., Cao, J.: Pth moment exponential stability of stochastic recurrent neural networks with time-varying delays. Nonlinear Anal.: Real World Appl. 8, 1171–1185 (2007)
Sworder, D.D., Rogers, R.O.: An LQ-solution to a control problem associated with solar thermal central receiver. IEEE Trans. Autom. AC-28, 971–978 (1983)
Willsky, A.S., Rogers, B.C.: Stochastic stability research for complex power systems. DOE Contract, LIDS, Mass. Inst. Technol., Cambridge, MA, Rep. ET-76-C-01-2295 (1979)
Mao, X.: Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans. Autom. Control 47, 1604–1612 (2002)
Lou, X., Cui, B.: Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters. J. Math. Anal. Appl. 328, 316–326 (2007)
Wang, Z., Liu, Y., Yu, L., Liu, X.: Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356, 346–352 (2006)
Huang, H., Ho, D.W.C., Qu, Y.: Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Netw. 20, 799–809 (2007)
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE Conference on Decision and Control, pp. 2805–2810. Sydney, Australia (2000)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was jointly supported by the National Natural Science Foundation of China under Grant No. 60574043, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20070286003, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2006093.
Rights and permissions
About this article
Cite this article
Wang, G., Cao, J. & Liang, J. Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters. Nonlinear Dyn 57, 209–218 (2009). https://doi.org/10.1007/s11071-008-9433-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-008-9433-4