×

Impulsive control for a class of neural networks with bounded and unbounded delays. (English) Zbl 1194.93192

Summary: We study the problem of global exponential stability for a class of impulsive neural networks with bounded and unbounded delays and fixed moments of impulsive effect. We establish stability criteria by employing Lyapunov functions and Razumikhin technique. An illustrative example is given to demonstrate the effectiveness of the obtained results.

MSC:

93D20 Asymptotic stability in control theory
92B20 Neural networks for/in biological studies, artificial life and related topics
34H05 Control problems involving ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Akca, H.; Alassar, R.; Covachev, V.; Covacheva, Z.; Al-Zahrani, E., Continuous-time additive Hopfield-type neural networks with impulses, Journal of Mathematical Analysis and Applications, 290, 436-451 (2004) · Zbl 1057.68083
[2] Ahmad, S.; Stamova, I. M., Global exponential stability for impulsive cellular neural networks with time-varying delays, Nonlinear Analysis: TMA, 69, 786-795 (2008) · Zbl 1151.34061
[3] Arbib, M. A., Branins Machines and Mathematics (1987), Springer-Verlag: Springer-Verlag New York
[4] Arik, S.; Tavanoglu, V., Equilibrium analysis of delayed CNNs, IEEE Transactions on Circuits and Systems - I, 45, 168-171 (1998)
[5] Arik, S.; Tavanoglu, V., On the global asymptotic stability of delayed cellular neural networks, IEEE Transactions on Circuits and Systems - I, 47, 571-574 (2000) · Zbl 0997.90095
[6] Cao, J., On stability of delayed cellular neural networks, Physics Letters A, 261, 303-308 (1999) · Zbl 0935.68086
[7] Chen, Y., Global stability of neural networks with distributed delays, Neural Networks, 15, 867-871 (2002)
[8] Chua, L. O., CNN: A Paradigm for Complexity (1998), World Scientific: World Scientific Singapore · Zbl 0916.68132
[9] Chua, L. O.; Yang, L., Cellular neural networks: Theory, IEEE Transactions on Circuits and Systems, CAS, 35, 1257-1272 (1988) · Zbl 0663.94022
[10] Chua, L. O.; Yang, L., Cellular neural networks: Applications, IEEE Transactions on Circuits and Systems, CAS, 35, 1273-1290 (1988)
[11] Feng, C.; Plamondon, R., On the stability analysis of delayed neural networks systems, Neural Networks, 14, 1181-1188 (2001)
[12] Gopalsamy, K.; He, X., Stability in asymmetric Hopfield nets with transmission delays, Physica D, 76, 344-358 (1994) · Zbl 0815.92001
[13] Haykin, S., Neural Networks: A Comprehensive Foundation (1998), Prentice-Hall: Prentice-Hall Ehglewood Cliffs, NJ · Zbl 0828.68103
[14] Hopfield, J. J., Neurons with graded response have collective computational properties like those of two-state neurons, Proceedings National Academy of Science USA, 81, 3088-3092 (1984) · Zbl 1371.92015
[15] Huang, H.; Cao, J., On global asymptotic stability of recurrent neural networks with time-varying delays, Applied Mathematics and Computation, 142, 143-154 (2003) · Zbl 1035.34081
[16] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore, New Jersey, London · Zbl 0719.34002
[17] Marcus, C. M.; Westervelt, R. M., Stability of analog neural networks with delay, Physical Review A, 39, 347-359 (1989)
[18] Razumikhin, B. S., Stability of Systems with Retardation (1988), Nauka: Nauka Moscow, (in Russian) · Zbl 0145.32203
[19] Roska, T.; Wu, C. W.; Balsi, M.; Chua, L. O., Stability and dynamics of delay-type general cellular neural networks, IEEE Transactions on Circuits and Systems - I, 39, 487-490 (1992) · Zbl 0775.92010
[20] Stamov, G. T., Existence of almost periodic solutions for impulsive cellular neural networks, Rocky Mountain Journal of Mathematics, 4, 1271-1285 (2008) · Zbl 1178.34100
[21] Stamov, G. T.; Stamova, I. M., Almost periodic solutions for impulsive neural networks with delay, Applied Mathematical Modelling, 31, 1263-1270 (2007) · Zbl 1136.34332
[22] Stamova, I. M.; Stamov, G. T., Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics, Journal of Computational and Applied Mathematics, 130, 163-171 (2001) · Zbl 1022.34070
[23] Yan, J.; Shen, J., Impulsive stabilization of impulsive functional differential equations by Lyapunov-Razumikhin functions, Nonlinear Analysis, 37, 245-255 (1999) · Zbl 0951.34049
[24] Yang, Z.; Xu, D., Stability analysis of delay neural networks with impulsive effects, IEEE Transactions on Circuits and Systems - II, 52, 517-521 (2005)
[25] Yi, Z.; Peng, P. A.; Leung, K. S., Convergence analysis of cellular neural networks with unbounded delay, IEEE Transactions on Circuits and Systems - I, 48, 680-687 (2001) · Zbl 0994.82068
[26] Zhang, J., Globally exponential stability of neural networks with variable delays, IEEE Transactions on Circuits and Systems - I, 50, 288-291 (2003) · Zbl 1368.93484
[27] Zhang, J.; Suda, Y.; Iwasa, T., Absolutely exponential stability of a class of neural networks with unbounded delay, Neural Networks, 17, 391-397 (2004) · Zbl 1074.68057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.