×

Improved delay-dependent stability criterion for neural networks with time-varying delay. (English) Zbl 1225.34080

A class of neural networks with time-varying delay is studied. The authors prove a delay-dependent asymptotic stability criterion for such nets by means of a Lyapunov functional containing a triple-integral term. Numerical examples are provided in order to illustrate the obtained theoretical results.

MSC:

34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cao, J. D.; Wang, L., Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Netw., 13, 457-463 (2002)
[2] Arik, S., Global asymptotic stability of a larger class of neural networks with constant time delay, Phys. Lett. A, 311, 504-511 (2002) · Zbl 1098.92501
[3] Cao, J. D.; Wang, J., Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I, 52, 2, 417-426 (2005) · Zbl 1374.93285
[4] Park, J. H.; Kwon, O. M., Further results on state estimation for neural networks of neutral-type with time-varying delay, Appl. Math. Comput., 208, 69-75 (2009) · Zbl 1169.34334
[5] Samli, R.; Arik, S., New results for global stability of a class of neutral-type neural systems with time delays, Appl. Math. Comput., 210, 564-570 (2009) · Zbl 1170.34352
[6] Tian, J. K.; Zhou, X. B., Improved asymptotic stability criteria for neural networks with interval time-varying delay, Expert Syst. Appl., 37, 7521-7525 (2010)
[7] Kwon, O. M.; Park, J. H., Exponential stability analysis for uncertain neural networks with interval time-varying delays, Appl. Math. Comput., 212, 530-541 (2009) · Zbl 1179.34080
[8] He, Y.; Liu, G. P.; Rees, D., New delay-dependent stability criteria for neural networks with time-varying delay, IEEE Trans. Neural Netw., 18, 310-314 (2007)
[9] He, Y.; Liu, G.; Rees, D.; Wu, M., Stability analysis for neural networks with time-varying interval delay, IEEE Trans. Neural Netw., 18, 1850-1854 (2007)
[10] Hua, C. C.; Long, C. N.; Guan, X. P., New results on stability analysis of neural networks with time-varying delays, Phys. Lett. A, 352, 335-340 (2006) · Zbl 1187.34099
[11] Kwon, O. M.; Park, J. H.; Lee, S. M., On robust stability for uncertain neural networks with interval time-varying delays, IET Control Theory Appl., 2, 625-634 (2008)
[12] Chen, Y.; Wu, Y., Novel delay-dependent stability criteria of neural networks with time-varying delay, Neurocomputing, 72, 1065-1070 (2009)
[13] Sun, J.; Liu, G. P.; Chen, J.; Rees, D., Improved stability criteria for neural networks with time-varying delay, Phys. Lett. A, 373, 342-348 (2009) · Zbl 1227.92003
[14] Qian, W.; Li, T.; Cong, S.; Fei, S., Improved stability analysis on delayed neural networks with linear fractional uncertainties, Appl. Math. Comput., 217, 3596-3606 (2010) · Zbl 1209.34087
[15] Kwon, O. M.; Park, J. H., Improved delay-dependent stability criterion for neural networks with time-varying delays, Phys. Lett. A, 373, 529-535 (2009) · Zbl 1227.34030
[16] Song, Q. K.; Zhao, Z. J.; Li, Y. M., Global exponential stability of BAM neural networks with distributed delays and reaction diffusion terms, Phys. Lett. A, 335, 213-225 (2005) · Zbl 1123.68347
[17] Arik, S.; Tavsanoglu, V., Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing, 68, 161-176 (2005)
[18] Arik, S., Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays, Phys. Lett. A, 351, 85-91 (2006) · Zbl 1234.34048
[19] Zhou, Q.; Wan, L., Global robust asymptotic stability analysis of BAM neural networks with time delay and impulse: an LMI approach, Appl. Math. Comput., 216, 1538-1545 (2010) · Zbl 1200.34088
[20] Liao, X. F.; Chen, G.; Sanchez, E. N., Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Netw., 15, 855-866 (2002)
[21] Mahmoud, M. S.; Ismail, A., Improved results on robust exponential stability criteria for neutral-type delayed neural networks, Appl. Math. Comput., 217, 3011-3019 (2010) · Zbl 1213.34084
[22] Li, C. D.; Feng, G., Delay-interval-dependent stability of recurrent neural networks with time-varying delay, Neurocomputing, 72, 1179-1183 (2009)
[23] Hu, L.; Gao, H.; Zheng, W., Novel stability of cellular neural networks with interval time-varying delay, Neural Netw., 21, 1458-1463 (2008) · Zbl 1254.34102
[24] Xu, S.; Lam, J., A new approach to exponential stability analysis of neural networks with time-varying delays, Neural Netw., 19, 76-83 (2006) · Zbl 1093.68093
[25] Zhao, H.; Cao, J., New conditions for global exponential stability of cellular neural networks with delays, Neural Netw., 18, 1332-1340 (2005) · Zbl 1083.68108
[26] Wang, Z.; Liu, Y.; Li, M.; Liu, X., Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans. Neural Netw., 17, 814-820 (2006)
[27] Guo, Z.; Huang, L., LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations, Appl. Math. Comput., 215, 889-900 (2009) · Zbl 1187.34098
[28] Park, J. H.; Kwon, O. M., On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays, Appl. Math. Comput., 199, 435-446 (2008) · Zbl 1149.34049
[29] Guo, Z.; Huang, L., LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations, Appl. Math. Comput., 215, 889-900 (2009) · Zbl 1187.34098
[30] Mou, S.; Gao, H.; Lam, J.; Qiang, W., New criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay, IEEE Trans. Neural Netw., 19, 532-535 (2008)
[31] Boyd, S.; Ghaoui, L. EL.; Feron, E.; Balakrishnam, V., Linear Matrix Inequalities in Systems and Control (1994), SIMA: SIMA Philadelphia
[32] Kwon, O. M.; Park, J. H., New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays, Appl. Math. Comput., 205, 417-427 (2008) · Zbl 1162.34060
[33] Kwon, O. M.; Park, J. H., Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays, J. Franklin Inst., 345, 766-778 (2008) · Zbl 1169.93400
[34] Ji, D. H.; Koo, J. H.; Won, S. C.; Lee, S. M.; Park, J. H., Passivity-based control for Hopfield neural networks using convex representation, Appl. Math. Comput., 217, 6168-6175 (2011) · Zbl 1209.93056
[35] Lee, S. M.; Kwon, O. M.; Park, J. H., A novel delay-dependent criterion for delayed neural networks of neutral type, Phys. Lett. A, 374, 1843-1848 (2010) · Zbl 1236.92007
[36] Lee, S. M.; Kwon, O. M.; Park, J. H., A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov-Krasovskii function, Chin. Phys. B, 19 (2010), (050507) 1-6
[37] Kwon, O. M.; Lee, S. M.; Park, J. H., Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays, Phys. Lett. A, 374, 1232-1241 (2010) · Zbl 1236.92006
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.