Abstract
The problem of global exponential stability of cellular neural networks with time-varying delays is discussed by employing a method of delay differential inequality. A simple sufficient condition is given for global exponential stability of the cellular neural networks with time-varying delays. The result obtained here improves some results in the previous works.
Keywords
- Equilibrium Point
- Exponential Stability
- Variable Delay
- Cellular Neural Network
- Global Asymptotic Stability
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The project supported by the National Natural Science Foundation of China (grant no. 60403001.) and China Postdoctoral Science Foundation (grant no.200303448).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory and Applications. IEEE Trans.Circuits Syst. I 35, 1257–1290 (1988)
Roska, T., Boros, T., Thiran, P., Chua, L.O.: Detecting Simple Motion Using Cellular Neural Networks. In: Proc.1990 IEEE Int. Workshop on Cellular Neural Networks and their Applications, pp. 127–138 (1990)
Zhang, Y., Zhong, S.M., Li, Z.L.: Periodic Solutions and Stabiltiy of Hopfield Neural Networks with Variable Delays. Int. J. Syst. Sci. 27, 895–901 (1996)
Qiang, Z., Ma, R., Chao, W., Jin, X.: On the Global Stability of Delayed Neural Networks. IEEE Trans. Automatic Control 48, 794–797 (2003)
Zhang, Q., Wei, X.P., Xu, J.: Global Exponential Convergence Analysis of Delayed Neural Networks with Time-Varying Delays. Phys. Lett. A 318, 537–544 (2003)
Zhang, Q., Wei, X.P., Xu, J.: On Global Exponential Stability of Delayed Cellular Neural Networks with Time-Varying Delays. Appl. Math. Comput. 162, 679–686 (2005)
Zhang, Q., Wei, X.P., Xu, J.: Delay-Dependent Exponential Stability of Cellular Neural Networks with Time-Varying Delays. Chaos, Solitons & Fractals 23, 1363–1369 (2005)
Zhang, J.: Globally Exponential Stability of Neural Networks with Variable Delays. IEEE Trans. Circuits Syst. I 50, 288–290 (2003)
Lu, H.: On Stability of Nonlinear Continuous-Time Neural Networks with Delays. Neural Networks 13, 1135–1143 (2000)
Xu, D., Zhao, H., Zhu, H.: Global Dynamics of Hopfield Neural Networks Involving Variable Delays. Comput. Math. Applicat. 42, 39–45 (2001)
Zhou, D., Cao, J.: Globally Exponential Stability Conditions for Cellular Neural Networks with Time-Varying Delays. Appl. Math. Comput. 131, 487–496 (2002)
Liao, X., Chen, G., Sanchez, E.N.: LMI-Based Approach for Asymptotically Stability Analysis of Delayed Neural Networks. IEEE Trans. Circuits Syst. I 49, 1033–1039 (2002)
Joy, M.: Results Concerning the Absolute Stability of Delayed Neural Networks. Neural Networks 13, 613–616 (2000)
Cao, J., Wang, J.: Global Asymptotic Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Syst. I 50, 34–44 (2003)
Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Science. Academic Press, London (1979)
Tokumarn, H., Adachi, N., Amemiya, T.: Macroscopic Stability of Interconnected Systems. In: 6th IFAC Congr., Paper ID44.4, pp. 1–7 (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Q., Zhou, D., Wang, H., Wei, X. (2005). Global Exponential Stability of Cellular Neural Networks with Time-Varying Delays. In: Wang, L., Chen, K., Ong, Y.S. (eds) Advances in Natural Computation. ICNC 2005. Lecture Notes in Computer Science, vol 3610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539087_52
Download citation
DOI: https://doi.org/10.1007/11539087_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28323-2
Online ISBN: 978-3-540-31853-8
eBook Packages: Computer ScienceComputer Science (R0)