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Volume 25 Issue 10
Oct.  2003
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Tan Xiaohui, Zhang Jiye, Yang Yiren. Study on global exponential stability of neural networks and its convergence estimate[J]. Journal of Electronics & Information Technology, 2003, 25(10): 1361-1366.
Citation: Tan Xiaohui, Zhang Jiye, Yang Yiren. Study on global exponential stability of neural networks and its convergence estimate[J]. Journal of Electronics & Information Technology, 2003, 25(10): 1361-1366.

Study on global exponential stability of neural networks and its convergence estimate

  • Received Date: 2002-04-27
  • Rev Recd Date: 2002-10-08
  • Publish Date: 2003-10-19
  • In this paper, the existence, uniqueness and global exponential stability of the equilibrium point of a class of Hopfield neural networks are investigated by using Liapunov direct method. Lipschitz continuous activations are considered and the limit on self-feedback is released. It can be nonlinear instead of linear in this paper. And under this condition, some sufficient conditions and convergence estimate for global exponential stability of neural networks are obtained.
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  • Zhang Jiye, Yang Yiren, Global stability analysis of bi-directional associative memory neural networks with time delay [J], International Journal of Circuit Theory and Application, 2001,29(3), 185-196.[2]Qiao Hong, Peng Jigen, Xu Zong-Ben, Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks [J], IEEE Trans. on Neural Networks, 2001,12(2), 360-370.[3]M. Forti, A. Tesi, New conditions for global stability of neural networks with application to linear and quadratic programming problems [J], IEEE Trans. on Circuits and Systems-I, 1995, 42(7),354-366.[4]Liang Xue-Bin, Si Jennie, Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem [J], IEEE Trans.on Neural Networks, 2001, 12(2), 349-359.[5]Chen Tianping, Amari Shun Ichi, Stability of asymmetric Hopfield networks [J], IEEE Trans.[J]. on Neural Networks.2001,12:159-[6]廖晓昕,Hopfield神经网络的稳定性[J],中国科学(A),1993,23(10),1025-1035.[7]梁学斌,吴立德,Hopfield型神经网络的全局指数稳定性及其应用[J],中国科学(A),1995,25(5),523-532.[8]梁学斌,吴立德,连续反馈联想记忆的吸引域和指数收敛速度的估计及其应用[J],电子科学学刊,1996,18(1),1-6.[9]梁学斌,吴立德,Hopfield连续联想记忆的吸引域和指数收敛速度的估计及其应用[J],电子学报,1996,24(1),40-43.[10]周冬明,曹进德,李继彬,连续反馈联想记忆的吸引域和指数收敛速度的估计[J],应用数学和力学,2001,23(3),275-279.[11]张强,许进,细胞神经网络的全局指数稳定性[J],电子科学学刊,2000,22(5),434-438. [12]Liang Xue-Bin, Wang Jun, An additive diagonal-stability condition for absolute exponential stability of a general class of neural networks[J], IEEE Trans. on Circuits and Systems-I, 2001,48(11), 1308-1317.[12]舒仲周,张继业,曹登庆,运动稳定性[M],北京,中国铁道出版社,2001,202-215.[13]D. Hershkowitz, Recent directions in matrix stability [J], Linear Algebra and Its Applications,July 1, 1992, Vol.171, 161-186.
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