Abstract
A method is proposed for asymptotic stability analysis of neutral neural networks with delayed state. The delay is assumed unknown, but constant. Sufficient conditions on delay-independent asymptotic stability are given in terms of the existence of symmetric and positive definite solutions of a constant Riccati algebraic matrix equation coupled with a discrete Lyapunov equation.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cao, J.D., Li, Q.: On the exponential stability and periodic solution of delayed cellular neural networks. J. Math. Anal. and Appl. 252(1), 50–64 (2000)
Curt, W.: Reactive Molecules: The Neutral Reactive Intermediates in Organic Chemistry. Wilay Press, New York (1984)
Fu, C.J., He, H.L., Liao, X.X.: Globally Stable Periodic State of Delayed Cohn-Grossberg Neural Networks. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 276–281. Springer, Heidelberg (2005)
Hale, J.K., Verduyn Lunel, S.M.: Introduation to Functional Differential Equations. In: Applied Math. Sciences, vol. 99. Springer, New York (1991)
He, H.L., Wang, Z.S., Liao, X.X.: Stability Analysis of Uncertain Neural Networks with Linear and Nonlinear Time Delays. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 199–202. Springer, Heidelberg (2005)
Liao, X.X., Xiao, D.M.: Globally Exponential Stability of Hopfield Neural Networks with Time-varying Delays. ACTA Electronica Sinica 28(1), 87–90 (2000)
Liao, X.X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE Trans. Circuits and Systems I. 50(2), 268–275 (2003)
Shen, Y., Zhao, G.Y., Jiang, M.H., Mao, X.R.: Stochastic Lotka-Volterra Competitive Systems with Variable Delay. In: Huang, D.-S., Zhang, X.-P., Huang, G.-B. (eds.) ICIC 2005. LNCS, vol. 3645, pp. 238–247. Springer, Heidelberg (2005)
Shen, Y., Zhao, G.Y., Jiang, M.H., Hu, S.G.: Stochastic High-order Hopfield Neural Networks. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3610, pp. 740–749. Springer, Heidelberg (2005)
Zeng, Z.G., Wang, J., Liao, X.X.: Global Exponential Stability of A General Class of Recurrent Neural Networks with Time-varying Delays. IEEE Trans. Circuits and Syst. I 50(10), 1353–1358 (2003)
Zeng, Z.G., Wang, J., Liao, X.X.: Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. Circuits and Syst. I 51(11), 2313–2324 (2004)
Shen, Y., Jiang, M.H., Liao, X.X.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-varying Delays and Continuously Distributed Delays. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 156–161. Springer, Heidelberg (2005)
Zhang, Y.M., Guo, L., Wu, L.Y., et al.: On Stochastic Neutral Neural Networks. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 69–74. Springer, Heidelberg (2005)
Zhang, Y.M., Shen, Y., Liao, X.X.: Exponential for Stochastic Interval Delayed Hopfield Neural Networks. Control Theory and Applications 20(12), 1299–1300 (2003)
Wang, Z.S., He, H.L., Liao, X.X.: Stability Analysis of Uncertain Neural Networks with Delay. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3173, pp. 44–48. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
He, H., Liao, X. (2006). Stability Analysis of Neutral Neural Networks with Time Delay. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_22
Download citation
DOI: https://doi.org/10.1007/11759966_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34439-1
Online ISBN: 978-3-540-34440-7
eBook Packages: Computer ScienceComputer Science (R0)