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一类具混合时滞随机神经网络稳定性的推广与应用

The Promotion and Application of Stability for a General Class of Stochastic Neural Networks with Mixed Time Delays
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摘要 将一类具有混合时滞随机神经网络均方渐近稳定的判据推广到不确定神经网络的鲁棒稳定性,所导出的判据都表示为线性矩阵不等式(LMI)的形式,可通过使用一些标准的数值方法求解.最后给出了一个简单的例子说明所提出的判定条件的有效性和可应用性. A linear matrix inequality （LMI） approach is developed to derive the criteria for the asymptotic stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox and expressed in form of LMI. In this paper, the results are extended to uncertain stochastic neural networks with Markovian jumping parameters and mixed delays. Finally, a simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.
作者 张金
机构地区 宿迁高等师范学校数学系
出处 《数学的实践与认识》 CSCD 北大核心 2014年第7期254-259,共6页 Mathematics in Practice and Theory
基金 宿迁高等师范学校科研基金(2013)
关键词 随机神经网络 不确定神经网络 混合时滞 鲁棒稳定性 线性矩阵不等式 stochastic neural networks uncertain neural networks mixed time delaysrobust stability linear matrix inequality
分类号 TP183 [自动化与计算机技术—控制理论与控制工程]
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参考文献12

  • 1Wang Z, Liu Y and Liu X. On global asymptotic stability of neural networks with discrete and distributed delays[J]. Physics Letters A, 2005, 345(4-6): 299-308.
  • 2Huang H, Ho D W C, and Lam J. Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays[J]. IEEE Trans Circuits and Systems: Part II, 2005, 52(5): 251-255.
  • 3Wang Z, Liu Y, Li M, and Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays[J]. IEEE Trans Neural Networks, 2006, 17(3): 814-820.
  • 4Wang Z, Liu Y, Fraser K, and Liu X. Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays[J]. Physics Letters A, 2006, 354(4): 288-297.
  • 5Casey M P. The dynamics of discrete-time computation with application to recurrent neural net- works and finite state machine extraction[J]. Neural Comput, 1996, 8(6): 1135-1178.
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  • 9张金.具混合时滞的随机神经网络的稳定性分析[J].苏州大学学报（自然科学版）,2011,27(2):16-22. 被引量：3
  • 10Shi P, Zhang J, Qiu J, Xing L. New global asymptotic stability criterion for neural networks with discrete and distributed delays[J]. Proc IMechE J Syst Control Eng, 2006, 221(11), 129-135.

二级参考文献9

  • 1Huang H,Qu Y,Li H X.Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty[J].Physics Letters A,2005,345 (4/6):345-354.
  • 2Tino P,Cemansky M,Benuskova L.Markovian architectural bias of recurrent neural networks[J].IEEE Trans Neural Networks,2004,15(1):6-15.
  • 3Wang Z,Liu Y,Yu L,et al.Exponential stability of delayed recurrent neural networks with Markovian jumping parameters[J].Physics Letters A,2006,356(4/5):346 -352.
  • 4Skorohod A V.Asymptotic methods in the theory of stochastic differential equations[M].Providence RI:Amer Math Soc,1989.
  • 5Wang Z,Liu Y,Liu X.On global asymptotic stability of neural networks with discrete and distributed delays[J].Physics Letters A,2005,345 (4/6):299-308.
  • 6Huang H,Ho D W C,Lam.J.Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays[J].IEEE Trans Circuits and Systems:Part Ⅱ,2005,52(5):251 -255.
  • 7Wang Z,Liu Y,Li M,et al.Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays[J].IEEE Trans Neural Networks,2006,17(3):814 -820.
  • 8Wang Z,Liu Y,Fraser K,et al.Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays[J].Physics Letters A,2006,354(4):288 -297.
  • 9Casey M P.The dynamics of discrete-time computation with application to recurrent neural networks and finite state machine extraction[J].Neural Comput,1996,8(6):1135-1178.

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数学的实践与认识
2014年 第7期

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