Abstract
This paper deals with the problem of stability criterion of discrete-time recurrent neural networks with periodic delays. It is written as a discrete-time multi-switched liner system (DMSLS), applying the parameter and time dependent Lyapunov functions we obtain several new sufficient conditions and sufficient conditions for asymptotically stability of these systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cao, J.D., Yuan, K., Li, H.X.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Netw. 17(6), 1646–1651 (2006)
Li, T., Guo, L., Sun, C., Lin, C.: Further Results on Delay-Dependent Stability Criteria of Neural Networks With Time-Varying Delays. IEEE Trans. on Neural Networks 19(4), 726–730 (2008)
Huang, H., Feng, G., Cao, J.D.: Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans. on Neural networks 19(8), 1329–1339 (2008)
Xiang, H., Yan, K.M., Wang, B.Y.: Existence and global exponential stability of periodic solution for delayed discrete high-order Hopfield-type neural networks. Physics Letters A 352, 341–349 (2006)
Xiang, H., Yan, K.M., Wang, B.Y.: Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Discrete Dynamics in Nature and Society 2005(3), 281–297 (2005)
Huang, C.X., He, Y.G., Huang, L.H., Lai, M.Y.: Global exponential periodicity of three-unit neural networks in a ring with time-varying delays. Neurocomputing 71, 1595–1603 (2008)
Jiang, H., Cao, J.D.: Global exponential stability of periodic neural networks with time-varying delays. Neurocomputing 70, 343–350 (2006)
Shao, Y., Dai, B.: The existence of exponential periodic attractor of impulsive BAM neural network with periodic coefficients and distributed delays. Neurocomputing 73, 3123–3131 (2010)
Liu, Y., You, Z., Cao, L.: On the almost periodic solution of generalized Hopfield neural networks with time-varying delays. Neurocomputing 69, 1760–1767 (2006)
Liu, B., Huang, L.: Existence and exponential stability of almost periodic solutions for Hopfield neural networks with delays. Neurocomputing 68, 196–207 (2005)
Cao, J.D., Wang, J.: Global Exponential Stability and Periodicity of Recurrent Neural Networks With Time Delays. IEEE Trans. on circuits and syst. I 52, 920–931 (2005)
Lou, X., Cui, B.: Delay-Dependent Criteria for Global Robust Periodicity of Uncertain Switched Recurrent Neural Networks With Time-Varying Delay. IEEE Trans. on Neural Networks 19, 549–557 (2008)
Huang, Z., Wang, X., Feng, C.: Multiperiodicity of Periodically Oscillated Discrete-Time Neural Networks with Transient Excitatory Self-Connections and Sigmoidal Nonlinearities. IEEE Trans. on Neural Networks 21, 1643–1655 (2010)
Allegretto, W., Papini, D., Forti, M.: Common Asymptotic Behavior of Solutions and Almost Periodicity for Discontinuous, Delayed, and Impulsive Neural Networks. IEEE Trans. on Neural Networks 21, 1110–1125 (2010)
Zhang, L., Zhang, Y., Yu, J.: Multiperiodicity and Attractivity of Delayed Recurrent Neural Networks With Unsaturating Piecewise Linear Transfer Functions. IEEE Trans. on Neural Networks 19, 158–167 (2008)
Chen, B., Wang, J.: Global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays. IEEE Trans. on Neural Networks 16(6), 1440–1449 (2005)
Wu, X.R., Wang, Y.N., Huang, L.H., Zuo, Y.: Robust exponential stability criterion for uncertain neural network swith discontinuous activation functions and time-varying delay. Neurocomputing 73, 1265–1271 (2010)
Song, Q., Cao, J.D.: Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays. Discrete Dynamics in Nature and Society (2010), Article ID 810408, 19 pages (2010)
Arzen, K.E., Bicchi, A., Hailes, S., Johansson, K.H., Lygeros, J.: On the design and control of wireless networked embedded systems. In: Proceedings of the 2006 IEEE Computer Aided Control Systems Design Symposium, Munich, Germany (2006)
Hetel, L., Daafouz, J., Iung, C.: Equivalence between the LyapunovCKrasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems. Nonlinear Analysis: Hybrid Systems 2, 697–705 (2008)
Xu, J., Cao, Y., Sun, Y., Tang, J.: Absolute Exponential Stability of Recurrent Neural Networks With Generalized Activation Function. IEEE Trans. on Neural Networks 19(6), 1075–1089 (2008)
Daafouz, J., Riedinger, P., Iung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. on Automatic Control 47(11), 1883–1887 (2002)
Li, J., Diao, Y.F., Li, M.D., Yin, X.: Stability analysis of Discrete Hopfield Neural Networks with the nonnegative definite monotone increasing weight function matrix. Discrete Dynamics in Nature and Society 2009,Article ID 673548, 10 (2009)
Li, J., Diao, Y., Mao, J., Zhang, Y., Yin, X.: Stability Analysis of Discrete Hopfield Neural Networks with Weight Function Matrix. In: Kang, L., Cai, Z., Yan, X., Liu, Y. (eds.) ISICA 2008. LNCS, vol. 5370, pp. 760–768. Springer, Heidelberg (2008)
Li, J., Wu, W.G., Yuan, J.M., Tan, Q.R., Yin, X.: Delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay. Discrete Dynamics in Nature and Society 2010, Article ID 347129, 16 (2010)
Li, J., Yang, J., Wu, W.G.: Stability analysis of discrete Hopfield neural networks with column arbitrary-dominant weight matrix. Neurocomputing (revised manuscript submitted to, 2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yin, X., Wu, W., Tan, Q. (2011). Stability Criterion of Discrete-Time Recurrent Neural Networks with Periodic Delays. In: Lu, BL., Zhang, L., Kwok, J. (eds) Neural Information Processing. ICONIP 2011. Lecture Notes in Computer Science, vol 7064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24965-5_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-24965-5_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24964-8
Online ISBN: 978-3-642-24965-5
eBook Packages: Computer ScienceComputer Science (R0)