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Stability analysis of static recurrent neural networks with interval time-varying delay. (English) Zbl 1329.93119
Summary: The problem of stability analysis of static recurrent neural networks with interval time-varying delay is investigated in this paper. A new Lyapunov functional which contains some new double integral and triple integral terms are introduced. Information about the lower bound of the delay is fully used in the Lyapunov functional. Integral and double integral terms in the derivative of the Lyapunov functional are divided into some parts to get less conservative results. Some sufficient stability conditions are obtained in terms of linear matrix inequality (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.

MSC:
93D20 Asymptotic stability in control theory
34K20 Stability theory of functional-differential equations
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[1] Liu, G. P., Nonlinear identification and control: A neural network approach, (2001), Springer London · Zbl 0983.93001
[2] Mandic, D. P.; Chambers, J. A., Recurrent neural networks for prediction: learning algorithms, architectures, and stability, (2001), Wiley New York
[3] Liang, J.; Cao, J. D., Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays, Phys. Lett. A, 314, 2005, 434-442, (2003) · Zbl 1052.82023
[4] Cao, J. D.; Wang, J., Exponential stability and periodicity of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I Reg. Pap., 52, 5, 920-931, (2005) · Zbl 1374.34279
[5] He, Y.; Liu, G. P.; Rees, D., New delay-dependent stability criteria for neural networks with time-varying delay, IEEE Trans. Neural Networks, 18, 1, 310-314, (2007)
[6] He, Y.; Liu, G. P.; Rees, D., Stability analysis for neural networks with time-varying interval delay, IEEE Trans. Neural Networks, 18, 6, 1850-1854, (2007)
[7] Li, C.; Feng, G., Delay-interval-dependent stability of recurrent neural networks with time-varying delay, Neurocomputing, 72, 1179-1183, (2009)
[8] Li, T.; Yao, X.; Wu, L.; Li, J., Improved delay-dependent stability results of recurrent neural networks, Appl. Math. Comput., 218, 9983-9991, (2012) · Zbl 1253.34067
[9] Mahmoud, M. S.; Xia, Y., Improved exponential stability analysis for delayed recurrent neural networks, J. Franklin Inst., 348, 2, 201-211, (2011) · Zbl 1214.34062
[10] Park, Ju. H.; Cho, H. J., A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays, Chaos Solitons Fract., 33, 436-442, (2007) · Zbl 1142.34379
[11] Park, Ju. 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
[12] Rakkiyappan, R.; Balasubramaniam, P., Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays, Appl. Math. Comput., 198, 2, 526-533, (2008) · Zbl 1144.34375
[13] Shao, J.-L.; Huang, T.-Z.; Wang, X.-P., Further analysis on global robust exponential stability of neural networks with time-varying delays, Commun. Nonlinear Sci. Numer. Simul., 17, 1117-1124, (2012) · Zbl 1239.93091
[14] Wang, Y.; Yang, C.; Zuo, Z., On exponential stability analysis for neural networks with time-varying delays and general activation functions, Commun. Nonlinear Sci. Numer. Simul., 17, 1447-1459, (2012) · Zbl 1239.92005
[15] Yu, J.; Zhang, K.; Fei, S., Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay, Nonlinear Anal. Real World Appl., 11, 207-216, (2010) · Zbl 1183.93108
[16] Zhang, Y.; Yue, D.; Tian, E., New stability criteria of neural networks with interval time-varying delay: a piecewise delay method, Appl. Math. Comput., 208, 249-259, (2009) · Zbl 1171.34048
[17] Kwon, O. M.; Park, Ju H.; Lee, S. M.; Cha, E. J., A new augmented Lyapunov-krasovskii functional approach to exponential passivity for neural networks with time-varying delays, Appl. Math. Comput., 217, 24, 10231-10238, (2011) · Zbl 1225.93096
[18] Ji, D. H.; Koo, J. H.; Won, S. C.; Lee, S. M.; Park, Ju H., Passivity-based control for Hopfield neural networks using convex representation, Appl. Math. Comput., 217, 13, 6168-6175, (2011) · Zbl 1209.93056
[19] Kwon, O. M.; Lee, S. M.; Park, Ju H.; Cha, E. J., New approaches on stability criteria for neural networks with interval time-varying delays, Appl. Math. Comput., 218, 19, 9953-9964, (2012) · Zbl 1253.34066
[20] Zheng-Guang, Wu.; Shi, Peng; Hongye, Su.; Chu, Jian, Passivity analysis for discrete-time stochastic Markovian jump neural networks with mixed time-delays, IEEE Trans. Neural Networks, 22, 10, 1566-1575, (2011)
[21] Zheng-Guang Wu, Peng Shi, Hongye Su, Jian Chu, Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled-data, IEEE Trans. Syst. Man Cybern. Part B: Cybern., http://dx.doi.org/10.1109/TSMCB.2012.2230441. · Zbl 1305.93202
[22] Lakshmanan, S.; Park, Ju. H.; Ji, D. H.; Jung, H. Y.; Nagamani, G., State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory, Nonlinear Dyn., 70, 1421-1434, (2012) · Zbl 1268.92012
[23] Balasubramaniama, P.; Lakshmanana, S.; Manivannanb, A., Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays, Chaos Solitons Fract., 4, 483-495, (2012) · Zbl 1268.93116
[24] Lakshmanan, S.; Balasubramaniam, P., New results of robust stability analysis for neutral type neural networks with time-varying delays and Markovian jumping parameters, Can. J. Phys., 89, 827-840, (2011)
[25] Xu, Z.; Qiao, H.; Peng, J.; Zhang, B., A comparative study on two modeling approaches in neural networks, Neural Networks, 17, 73-85, (2004) · Zbl 1082.68099
[26] Du, B.; Lam, J., Stability analysis of static recurrent neural networks using delay-partitioning and projection, Neural Networks, 22, 4, 343-347, (2009) · Zbl 1338.93311
[27] Shao, H., Delay-dependent stability for recurrent neural networks with time-varying delays, IEEE Trans. Neural Networks, 19, 9, 1647-1651, (2008)
[28] Zuo, Z.; Yang, C.; Wang, Y., A new method for stability analysis of recurrent neural networks with interval time-varying delay, IEEE Trans. Neural Networks, 21, 2, 339-344, (2010)
[29] Wu, Z.-G.; Lam, J.; Su, H.; Chu, J., Stability and dissipativity analysis of static neural networks with time delay, IEEE Trans. Neural Networks, 23, 2, 199-210, (2012)
[30] Liu, Y.; Wang, Z.; Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Networks, 19, 667-675, (2006) · Zbl 1102.68569
[31] Wang, Z.; Shu, H.; Liu, Y.; Ho, D. W.C.; Liu, X., Robust stability analysis of generalized neural networks with discrete and distributed time delays, Chaos Solitons Fract., 30, 886-896, (2006) · Zbl 1142.93401
[32] Sun, J.; Liu, G. P.; Chen, J.; Rees, D., Improved delay-range-dependent stability criteria for linear systems with time-varying delays, Automatica, 46, 2, 466-470, (2010) · Zbl 1205.93139
[33] Chen, J.; Sun, J.; Liu, G. P.; Rees, D., New delay-dependent stability criteria for neural networks with time-varying interval delay, Phys. Lett. A, 374, 43, 4397-4405, (2010) · Zbl 1238.82027
[34] K. Gu, An integral inequality in the stability problem of time-delay systems, in: the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 2805-2810.
[35] He, Y.; Wang, Q.-G.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 371-376, (2007) · Zbl 1111.93073
[36] Kim, J. H., Note on stability of linear systems with a time-varying delay, Automatica, 47, 2118-2121, (2011) · Zbl 1227.93089
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