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Mean square exponential stability of uncertain stochastic delayed neural networks. (English) Zbl 1217.92005

Summary: This letter concerns the mean square exponential stability of uncertain stochastic delayed neural networks. By applying Lyapunov functional method, new delay-dependent/independent mean square exponential stability criteria are derived in terms of linear matrix inequalities. Two examples are presented which show our result are less conservative than the existing stability criteria.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
68T05 Learning and adaptive systems in artificial intelligence
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[1] Marcus, C. M.; Westervelt, R. M., Phys. Rev. A, 39, 347 (1989)
[2] Cao, J., Phys. Lett. A, 270, 157 (2000)
[3] Cao, J., Phys. Lett. A, 267, 312 (2000)
[4] Xu, D.; Zhao, H.; Zhu, H., Comput. Math. Appl., 42, 39 (2001)
[5] Ye, H.; Michel, A. N., IEEE Trans. Circuits Syst.-I, 43, 532 (1996)
[6] Chen, W.-H.; Lu, X.; Liang, D.-Y., Phys. Lett. A, 358, 186 (2006)
[7] Chen, W.-H.; Lu, X.; Guan, Z.-H.; Zheng, W. X., IEEE Trans. Circuits Syst.-II, 53, 837 (2006)
[8] Chen, W.-H.; Guan, Z.-H.; Lu, X., Phys. Lett. A, 326, 355 (2004)
[9] Chen, W.-H.; Lu, X., Phys. Lett. A, 351, 53 (2006)
[10] Chen, W.-H.; Zheng, W. X., IEEE Trans. Circuits Syst.-I, 53, 644 (2006)
[11] Xu, S.; Lam, J.; Ho, D. W.C.; Zou, Y., IEEE Trans. Circuits Syst.-II, 53, 230 (2006)
[12] He, Y.; Wu, M.; She, J.-H., IEEE Trans. Circuits Syst.-II, 53, 553 (2006)
[13] He, Y.; Liu, G. P.; Rees, D., IEEE Trans. Neural. Networks., 18, 310 (2007)
[14] Haykin, S., Neural Networks (1994), Prentice Hall: Prentice Hall New York · Zbl 0828.68103
[15] Mao, X., Stochastic Differential Equations and Applications (1997), Ellis Horwood · Zbl 0884.60052
[16] Blythe, S.; Mao, X.; Liao, X., J. Franklin Inst., 338, 481 (2001)
[17] Wan, L.; Sun, J., Phys. Lett. A, 343, 306 (2005)
[18] Zhu, W.; Hu, J., Chaos Solitons Fractals, 29, 171 (2006)
[19] Wang, Z.; Shu, H.; Fang, J.; Liu, X., Nonlinear Anal.: Real World Appl., 7, 1119 (2006)
[20] Zhang, J.; Shi, P.; Qiu, J., Nonlinear Anal.: Real World Appl., 8, 1349 (2007)
[21] Huang, H.; Feng, G., Physica A, 381, 93 (2007)
[22] He, Y.; Wu, M.; H She, J.; P Liu, G., Syst. Control. Lett., 51, 57 (2004)
[23] He, Y.; Wang, Q. G.; Xie, L. H.; Lin, C., IEEE Trans. Automat. Control., 52, 293 (2007)
[24] Boyd, S.; Ghaoui, L. EI.; Feron, E.; Balakrishnan, V., Matrix Inequalities in Systems and Control Theory (1994), SIAM: SIAM Philadephia, PA
[25] Wang, Y.; Xie, L.; De Souza, C. E., Syst. Control. Lett., 19, 139 (1992)
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.