Abstract
In this paper, the global exponential stability is discussed for discrete-time bidirectional associative memory (BAM) neural networks with time varying delays. By the linear matrix inequality (LMI) technique and discrete Lyapunov functional combined with inequality techniques, a new global exponential stability criterion of the equilibrium points is obtained for this system. The proposed result is less restrictive than those given in the earlier literatures, and easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation example is used to demonstrate the effectiveness of our result.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kosko, B.: Adaptive Bi-directional Associative Memories. Appl. Opt. 26, 4947–4960 (1987)
Kosko, B.: Bi-directional Associative Memories. IEEE Trans. Syst. Man Cybernet 18, 49–60 (1988)
Hopfield, J.: Neurons with Graded Response have Collective Computational Properties like Those of Two-state Neurons. Proceedings of the National Academy of Sciences of the United States of America 81, 3088–3092 (1984)
Zhang, H.G., Wang, Z.S.: Stability Analysis of BAM Neural Networks with Time-varying Delays. Progress in Natural Science 17, 206–211 (2007)
Guan, H.X., Wang, Z.S., Zhang, H.G.: Stability Analysis of Uncertain Bi-directional Associative Memory Neural Networks with Variable Delays. Control Theory & Applications 25, 421–426 (2008)
Cui, B., Lou, X.: Global Asymptotic Stability of BAM Neural Networks with Distributed Delays and Reaction–diffusion Terms. Chaos, Solitons & Fractals 27, 1347–1354 (2006)
Cao, J., Dong, M.: Exponential Stability of Delayed Bidirectional Associative Memory Networks. Appl. Math. Comput. 135, 105–112 (2003)
Guan, H.X., Wang, Z.S., Zhang, H.G.: Robust Stability of BAM Neural Networks with Delays. J. Northeastern University (Natural Science) 28, 1069–1072 (2007)
‘Sheng, L., Yang, H.: Novel Global Robust Exponential Stability Criterion for Uncertain BAM Neural Networks with Time-varying Delays. Chaos, Solitons & Fractals (in press)
Liang, J., Cao, J.: Exponential Stability of Continuous-time and Discrete-time Bidirectional Associative Memory Networks with Delays. Chaos, Solitons & Fractals 22, 773–785 (2004)
Liang, J., Cao, J., Ho, D.W.C.: Discrete-time Bidirectional Associative Memory Neural Networks with Variable Delays. Phys. Lett. A 335, 226–234 (2005)
Liu, X., Tang, M., Martin, R., Liu, X.: Discrete-time BAM Neural Networks with Variable Delays. Phys. Lett. A 367, 322–330 (2007)
Gao, M., Cui, B.T.: Global Robust Exponential Stability of Discrete-time Interval BAM Neural Networks with Time-varying Delays. Appl. Math. Modell. (in press)
Huang, Y.S., Wu, C.W.: A Unifying Proof of Global Asymptotical Stability of Neural Networks with Delay. IEEE Trans. Circ. Syst. II: Express Briefs 52, 181–184 (2005)
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, R., Wang, Z., Feng, J., Jing, Y. (2009). Delay-Dependent Exponential Stability of Discrete-Time BAM Neural Networks with Time Varying Delays. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_51
Download citation
DOI: https://doi.org/10.1007/978-3-642-01507-6_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01506-9
Online ISBN: 978-3-642-01507-6
eBook Packages: Computer ScienceComputer Science (R0)