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Wang, Yangfan; Wang, Linshan

LMI-based approach for exponential robust stability of high-order Hopfield neural networks with time-varying delays. (English) Zbl 1244.93133

J. Appl. Math. 2012, Article ID 182745, 8 p. (2012).
Summary: This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

Cited in 3 Documents

MSC:

93D09 Robust stability
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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\textit{Y. Wang} and \textit{L. Wang}, J. Appl. Math. 2012, Article ID 182745, 8 p. (2012; Zbl 1244.93133)
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References:

[1] X. Liao and Y. Liao, “Stability of Hopfield-type neural networks. II,” Science in China. Series A. Mathematics, vol. 40, no. 8, pp. 813-816, 1997. · Zbl 0886.68115
[2] G. Wallis, “Stability criteria for unsupervised temporal association networks,” IEEE Transactions on Neural Networks, vol. 16, no. 2, pp. 301-311, 2005.
[3] C. Wang and D. J. Hill, “Deterministic learning and rapid dynamical pattern recognition,” IEEE Transactions on Neural Networks, vol. 18, no. 3, pp. 617-630, 2007.
[4] J. Cao and M. Xiao, “Stability and Hopf bifurcation in a simplified BAM neural network with two time delays,” IEEE Transactions on Neural Networks, vol. 18, no. 2, pp. 416-430, 2007.
[5] K. Gopalsamy and X. Z. He, “Stability in asymmetric Hopfield nets with transmission delays,” Physica D. Nonlinear Phenomena, vol. 76, no. 4, pp. 344-358, 1994. · Zbl 0815.92001
[6] L. Wang, “Comments on ”robust stability for interval Hopfield neural networks with time delay” by X. F. Liao,” IEEE Transactions on Neural Networks, vol. 13, no. 1, pp. 250-251, 2002.
[7] L. S. Wang, Delayed Recurrent Neural Networks, Science Press, Beijing, China, 2008. · Zbl 1220.35090
[8] D. Xu, H. Zhao, and H. Zhu, “Global dynamics of Hopfield neural networks involving variable delays,” Computers & Mathematics with Applications, vol. 42, no. 1-2, pp. 39-45, 2001. · Zbl 0990.34036
[9] P. P. Civalleri, M. Gilli, and L. Pandolfi, “On stability of cellular neural networks with delay,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 40, no. 3, pp. 157-165, 1993. · Zbl 0792.68115
[10] J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proceedings of the National Academy of Sciences of the United States of America, vol. 79, no. 8, pp. 2554-2558, 1982. · Zbl 1369.92007
[11] J. J. Hopfield, “Neurons with graded response have collective computational like those of two-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol. 81, pp. 3088-3092, 1984. · Zbl 1371.92015
[12] X. Liu and Q. Wang, “Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 1, pp. 71-79, 2008.
[13] Y. Wang, C. Lu, G. Ji, and L. Wang, “Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 3319-3325, 2011. · Zbl 1221.34204
[14] B. Xu, X. Liu, and X. Liao, “Global asymptotic stability of high-order Hopfield type neural networks with time delays,” Computers & Mathematics with Applications, vol. 45, no. 10-11, pp. 1729-1737, 2003. · Zbl 1045.37056
[15] M. Brucoli, L. Carnimeo, and G. Grassi, “Associative memory design using discrete-time second-order neural networks with local interconnections,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 44, no. 2, pp. 153-158, 1997. · Zbl 0874.68256
[16] E. B. Kosmatopoulos and M. A. Christodoulou, “Structural properties of gradient recurrent high-order neural networks,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 42, no. 9, pp. 592-603, 1995. · Zbl 0943.68510
[17] E. B. Kosmatopoulos, M. M. Polycarpou, M. A. Christodoulou, and P. A. Ioannou, “High-order neural network structures for identification of dynamical systems,” IEEE Transactions on Neural Networks, vol. 6, no. 2, pp. 422-431, 1995.
[18] A. Dembo, O. Farotimi, and T. Kailath, “High-order absolutely stable neural networks,” IEEE Transactions on Circuits and Systems, vol. 38, no. 1, pp. 57-65, 1991. · Zbl 0712.92002
[19] Y. Wang, P. Lin, and L. Wang, “Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1353-1361, 2012. · Zbl 1239.93081
[20] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. · Zbl 0816.93004
[21] S. G. Hu, Nonlinear Analysis and Methods, Huazhong University of Science and Technology, Wuhan, China, 1993.
[22] D. J. Guo, J. X. Sun, and Z. L. Liu, Functional Methods of Nonlinear Ordinary Differential Equations, Shandong Science Press, Jinan, China, 1995.
[23] L. Wang, R. Zhang, and Y. Wang, “Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays,” Nonlinear Analysis. Real World Applications, vol. 10, no. 2, pp. 1101-1113, 2009. · Zbl 1167.35404
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