不确定随机变时滞神经网络的全局渐进稳定性
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摘要
采用Ito’s微分公式和不等式分析技巧,研究了一类不确定随机变时滞神经网络的全局渐进稳定性问题.该模型同时考虑了神经网络模型的两种扰动因素,即随机扰动与不确定性扰动.不确定性参数是时变且范数有界的.通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了平衡点在均方根意义下的全局渐进稳定性判据,能够利用LMI工具箱很容易地进行检验.此外,仿真示例证明了结论的有效性.
By Ito^'s differential formula and combining the method of inequality analysis,the problem of stochastic asymptotical stability of a class of stochastic neural networks with time-varying delays and parameter uncertainties is investigated.There are two kinds of disturbances which are unavoidable to be considered in neural networks.The parameter uncertainties are time-varying and norm-bounded.The time-delay factors are unknown and time-varying with known bounds.Based on Lyapunov-Krasovskii functional and stochastic analysis approaches,some new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be stochastically asymptotically stable in the mean square for all admissible uncertainties.Numerical examples are given to demonstrate the usefulness of the proposed asymptotical stability criteria.
By Ito^'s differential formula and combining the method of inequality analysis,the problem of stochastic asymptotical stability of a class of stochastic neural networks with time-varying delays and parameter uncertainties is investigated.There are two kinds of disturbances which are unavoidable to be considered in neural networks.The parameter uncertainties are time-varying and norm-bounded.The time-delay factors are unknown and time-varying with known bounds.Based on Lyapunov-Krasovskii functional and stochastic analysis approaches,some new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be stochastically asymptotically stable in the mean square for all admissible uncertainties.Numerical examples are given to demonstrate the usefulness of the proposed asymptotical stability criteria.
引文
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[4]Liao X,Mao X.Exponential stability and instability of stochastic neural networks[J].Stochastic Analysis and Ap-plications,1996,14(2):165-185.
[5]Wan L,Sun J.Mean square exponential stability of stochastic delayed Hopfield neural networks[J].Physics Letters A,2005,343(4):306-318.
[6]Liu B,Liu X.Robust stability of uncertain discretei mpul-sive systems[J].IEEE Transactions on Circuits Systems II,2007,54(5):455-459.
[7]Mao X.Stochastic differential equations and their applica-tions[M].UK,Horwood:Chichester,1997.
[8]Zhang J,Shi P,Qiu J.Novel robust stability criteria for uncertain stochastic hopfield neural networks with ti me-varying delays[J].Nonlinear Analysis:Real World Appli-cations,2007,8(4):1349-1357.
[2]杨居义,易永宏.基于BP神经网络的地震预测研究[J].微电子学与计算机,2008,25(10):129-132.
[3]Blythe S,Mao X,Liao X.Stability of stochastic delay neural networks[J].Journal of the Franklin Institute,2001,338(4):481-495.
[4]Liao X,Mao X.Exponential stability and instability of stochastic neural networks[J].Stochastic Analysis and Ap-plications,1996,14(2):165-185.
[5]Wan L,Sun J.Mean square exponential stability of stochastic delayed Hopfield neural networks[J].Physics Letters A,2005,343(4):306-318.
[6]Liu B,Liu X.Robust stability of uncertain discretei mpul-sive systems[J].IEEE Transactions on Circuits Systems II,2007,54(5):455-459.
[7]Mao X.Stochastic differential equations and their applica-tions[M].UK,Horwood:Chichester,1997.
[8]Zhang J,Shi P,Qiu J.Novel robust stability criteria for uncertain stochastic hopfield neural networks with ti me-varying delays[J].Nonlinear Analysis:Real World Appli-cations,2007,8(4):1349-1357.
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