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Delay-independent stability analysis of Cohen-Grossberg neural networks. (English) Zbl 1030.92002
Summary: We discuss a class of Cohen-Grossberg neural networks with time delays and investigate their global asymptotic stability of the equilibrium points for this systems. By introducing a new type of Lyapunov functionals, a set of sufficient conditions guaranteeing the global asymptotic convergence are derived. Our criteria represent an extension of the existing results in the literature. Combined with linear matrix inequality techniques, a new generalized, linear matrix inequalities (LMI) based, criterion is obtained. The presented result is more easily to verify and turns out to be less restrictive than those given in the earlier literature.

MSC:
92B20 Neural networks for/in biological studies, artificial life and related topics
34D05 Asymptotic properties of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
Software:
LMI toolbox
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References:
[1] Arik, S., IEEE trans. neural networks, 13, 5, 1239, (2002)
[2] Arik, S.; Tavsanoglu, V., IEEE trans. circuits systems I fund. theory appl., 47, 4, 571, (2000)
[3] Belair, J., J. dynamics differential equations, 5, 607, (1993)
[4] Boyd, S., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia
[5] Cao, J., Phys. lett. A, 267, 312, (2000)
[6] Chen, T., Neural processing lett., 10, 3, 267, (1999)
[7] T. Chen, L. Rong, Robust global exponential stability of Cohen-Grossberg neural networks with time delays, IEEE Trans. Neural Networks, in press
[8] Chen, T.; Amari, S., IEEE trans. neural networks, 12, 1, 159, (2001)
[9] Cohen, M.; Grossberg, S., IEEE trans. systems man cybernet., SMC-13, 815, (1983)
[10] Feng, C.; Plamondon, R., Neural networks, 14, 1181, (2001)
[11] P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI control toolbox, for use with {\scMatlab}, 1995
[12] Gopalsamy, K.; He, X., Physica D, 76, 344, (1994)
[13] Hopfield, J., Proc. natl. acad. sci. U.S.A., 81, 3088, (1984)
[14] Hu, S.; Wang, J., IEEE trans. circuits systems I fund. theory appl., 49, 9, 1334, (2002)
[15] Joy, M., J. math. anal. appl., 232, 61, (1999)
[16] Liao, T.; Wang, F., IEEE trans. neural networks, 11, 6, 1481, (2000)
[17] Liao, X.; Chen, G.; Sanchez, E., Neural networks, 15, 855, (2002)
[18] Lu, W.; Chen, T., Neural comput., 15, 5, 1173, (2003)
[19] W. Lu, L. Rong, T. Chen, Global convergence of delayed neural network systems, Int. J. Neural Systems, in press
[20] Marcus, C.; Westervelt, R., Phys. rev. A., 39, 347, (1989)
[21] Qiao, H.; Peng, J.; Xu, Z., IEEE trans. neural networks, 12, 2, 360, (2001)
[22] Shampine, L.; Thompson, S., Appl. numer. math., 37, 441, (2001)
[23] Shampine, L.; Reichelt, M., SIAM J. sci. comput., 18, 1, (1997)
[24] van den Driessche, P.; Zou, X., SIAM J. appl. math., 58, 6, 1878, (1998)
[25] van den Driessche, P.; Wu, J.; Zou, X., Physica D, 150, 84, (2001)
[26] Wang, L.; Zou, X., Neural networks, 15, 415, (2002)
[27] Wang, L.; Zou, X., Physica D, 170, 162, (2002)
[28] Ye, H.; Michel, A.; Wang, K., Phys. rev. E, 51, 2611, (1995)
[29] Zhang, Y.; Heng, P.; Leung, K., IEEE trans. circuits systems I fund. theory appl., 48, 6, 680, (2001)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.