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State estimation for neural networks of neutral-type with interval time-varying delays. (English) Zbl 1166.34331

A class of neutral networks with interval time-varying delays described by a nonlinear delay differential equation of neutral-type is considered. The interval time-varying delay does not have the constraint that its derivative is less than 1. The neuron state is estimated via available output measurements such that the estimation error converges to zero. By constructing a suitable Lyapunov functional, a new condition for the existence of a state estimator for the networks is given in terms linear matrix inequality. The advantage of the proposed approach is that the resulting stability criterion can be used efficiently via existing numerical convex optimization algorithms. A numerical example is given to show the effectiveness of proposed method.

MSC:

34K35 Control problems for functional-differential equations
34K40 Neutral functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics

Software:

LMI toolbox
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References:

[1] Chua, L.; Yang, L., Cellular neural networks: theory and applications, IEEE Transactions on Circuits and Systems I, 35, 1257-1290 (1988)
[2] Hopfield, J. J., Neurons with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences, 81, 3088-3092 (1984) · Zbl 1371.92015
[3] Chen, C. J.; Liao, T. L.; Hwang, C. C., Exponential synchronization of a class of chaotic neural networks, Chaos, Solitons & Fractals, 24, 197-206 (2005) · Zbl 1060.93519
[4] Otawara, K.; Fan, L. T.; Tsutsumi, A.; Yano, T.; Kuramoto, K.; Yoshida, K., An artificial neural network as a model for chaotic behavior of a three-phase fluidized bed, Chaos, Solitons & Fractals, 13, 353-362 (2002) · Zbl 1073.76656
[5] Gopalsamy, K., Stability of artificial neural networks with impulses, Applied Mathematics and Computation, 154, 783-813 (2004) · Zbl 1058.34008
[6] Cao, J., Global asymptotic stability of neural networks with transmission delays, International Journal of Systems Science, 31, 313-1316 (2000) · Zbl 1080.93517
[7] Arik, S.; Tavsanoglu, V., On the global asymptotic stability of delayed cellular neural networks, IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications, 47, 571-574 (2000) · Zbl 0997.90095
[8] Cao, J.; Zhong, S.; Hu, Y., Global stability analysis for a class of neural networks with varying delays and control input, Applied Mathematics and Computation, 189, 1480-1490 (2007) · Zbl 1128.34046
[9] Wang, L., Stability of Cohen-Grossberg neural networks with distributed delays, Applied Mathematics and Computation, 160, 93-110 (2005) · Zbl 1069.34113
[10] Park, J. H., Further note on global exponential stability of uncertain cellular neural networks with variable delays, Applied Mathematics and Computation, 188, 850-854 (2007) · Zbl 1126.34376
[11] Arik, S., An analysis of global asymptotic stability of delayed cellular neural networks, IEEE Transactions on Neural Network, 13, 1239-1242 (2002)
[12] Park, J. H., Global exponential stability of cellular neural networks with variable delays, Applied Mathematics and Computation, 183, 2, 1214-1219 (2006) · Zbl 1115.34071
[13] Park, J. H., Further result on asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays, Applied Mathematics and Computation, 182, 2, 1661-1666 (2006) · Zbl 1154.92302
[14] Zhao, H.; Ding, N., Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays, Applied Mathematics and Computation, 183, 464-470 (2006) · Zbl 1117.34080
[15] Cho, H. J.; Park, J. H., Novel delay-dependent robust stability criterion of delayed cellular neural networks, Chaos, Solitons & Fractals, 32, 3, 1194-1200 (2007) · Zbl 1127.93352
[16] Park, J. H., An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays, Chaos, Solitons & Fractals, 32, 2, 800-807 (2007) · Zbl 1144.93023
[17] Park, J. H., A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos, Solitons & Fractals, 29, 2, 446-453 (2006) · Zbl 1121.92006
[18] Xu, S.; Lam, J.; Ho, D. W.C.; Zou, Y., Delay-dependent exponential stability for a class of neural networks with time delays, Journal of Computational and Applied Mathematics, 183, 16-28 (2005) · Zbl 1097.34057
[19] Park, J. H., Robust stability of bidirectional associative memory neural networks with time delays, Physics Letters A, 349, 6, 494-499 (2006)
[20] K.-W. Yu, C.-H. Lien, Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2007.01.002; K.-W. Yu, C.-H. Lien, Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2007.01.002
[21] J. Qiu, H. Yang, J. Zhang, Z. Gao, New robust stability criteria for uncertain neural networks with interval time-varying delays, Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2007.01.087; J. Qiu, H. Yang, J. Zhang, Z. Gao, New robust stability criteria for uncertain neural networks with interval time-varying delays, Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2007.01.087 · Zbl 1197.34141
[22] C. Peng, Y.-C. Tian, Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay, Journal of Computational and Applied Mathematics, in press, doi:10.1016/j.cam.2007.03.009; C. Peng, Y.-C. Tian, Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay, Journal of Computational and Applied Mathematics, in press, doi:10.1016/j.cam.2007.03.009 · Zbl 1136.93437
[23] Yue, D.; Peng, C.; Tang, G. Y., Guaranteed cost control of linear systems over networks with state and input quantisations, IEE Proceedings - Control Theory and Applications, 153, 6, 658-664 (2006)
[24] Qiu, J.; Cao, J., Delay-dependent robust stability of neutral-type neural networks with time delays, Journal of Mathematical Control Science and Applications, 1, 1, 179-188 (2007) · Zbl 1170.93364
[25] Xu, S.; Lam, J.; Ho, D. W.C.; Zou, Y., Delay-dependent exponential stability for a class of neural networks with time delays, Journal of Computational and Applied Mathematics, 183, 16-28 (2005) · Zbl 1097.34057
[26] Park, J. H.; Kwon, O. M.; Lee, S. M., LMI optimization approach on stability for delayed neural networks of neutral-type, Applied Mathematics and Computation, 196, 1, 236-244 (2008) · Zbl 1157.34056
[27] Kwon, O. M.; Park, Ju H.; Lee, S. M., On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays, Applied Mathematics and Computation, 197, 2, 864-873 (2008) · Zbl 1144.34052
[28] Park, J. H.; Park, C. H.; Kwon, O. M.; Lee, S. M., A new stability criterion for bidirectional associative memory neural networks of neutral-type, Applied Mathematics and Computation, 199, 2, 716-722 (2008) · Zbl 1149.34345
[29] Wang, Z.; Ho, D. W.C.; Liu, X., State estimation for delayed neural networks, IEEE Transaction on Neural Networks, 16, 279-284 (2005)
[30] H. Huang, G. Feng, J. Cao, An LMI approach to delay-dependent state estimation for delayed neural networks, Neurocomputing, doi:10.1016/j.neucom.2007.08.008; H. Huang, G. Feng, J. Cao, An LMI approach to delay-dependent state estimation for delayed neural networks, Neurocomputing, doi:10.1016/j.neucom.2007.08.008
[31] Park, J. H.; Kwon, O. M., Design of state estimator for neural networks of neutral-type, Applied Mathematics and Computation, 202, 1, 360-369 (2008) · Zbl 1142.93016
[32] Boyd, B.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory (1994), SIAM: SIAM Philadelphia
[33] K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of the IEEE CDC, Australia, 2000, pp. 2805-2810.; K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of the IEEE CDC, Australia, 2000, pp. 2805-2810.
[34] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., LMI Control Toolbox User’s Guide (1995), The Mathworks: The Mathworks Massachusetts
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