变时滞随机模糊细胞神经网络的全局指数稳定性
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摘要
通过构造合适的Lyapunov泛函,利用It微分算子和不等式的分析技巧研究一类变时滞随机模糊细胞神经网络平衡点的全局指数稳定性,得到了该模型全局指数稳定的一个时滞独立和一个时滞依赖的充分条件.最后通过数值算例验证结论的有效性.
Global exponential stability of equilibrium point of a class of stochastic fuzzy cellular neural networks with timevarying delays is studied by constructing proper Lyapunov functional,using the It differential formula and inequality technique. A delay-independent sufficient condition and a delay-dependent sufficient condition for the global exponential stability are obtained. Finally,an illustrative example is given to show the effectiveness of the obtained results.
Global exponential stability of equilibrium point of a class of stochastic fuzzy cellular neural networks with timevarying delays is studied by constructing proper Lyapunov functional,using the It differential formula and inequality technique. A delay-independent sufficient condition and a delay-dependent sufficient condition for the global exponential stability are obtained. Finally,an illustrative example is given to show the effectiveness of the obtained results.
引文
[1]YANG T,YANG L B,WU C W,et al.Fuzzy cellular neural network:theory[C]//Proceedings of IEEE International Workshop on Cellular Neural Networks and Application,1996:181-186.
[2]ZHANG Q H,XING R G.Global asymptotic stability of fuzzy cellular neural networks with time-varying delays[J].Physics Letters A,2008,327(22):3971-3978.
[3]刘振伟,张化光,佟绍成.一类时变时滞模糊细胞神经网络的时滞依赖指数稳定性判据[J].电子学报,2009,37(3):513-518.
[4]WANG J,LU J G.Global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms[J].Chaos,Solitons and Fractals,2008,38(3):878-885.
[5]周凤燕.随机时滞反应扩散广义细胞神经网络的均值指数稳定性[J].数学的实践与认识,2012,42(3):168-179.
[6]张伟伟,王林山.S-分布时滞随机区间细胞神经网络的全局指数鲁棒稳定性[J].山东大学学报:理学版,2012,47(3):87-92.
[7]张千宏,杨利辉,刘璟忠.变时滞随机模糊细胞神经网络的均方指数稳定性分析[J].安徽大学学报:自然科学版,2013,37(1):13-17.
[8]李亚军,邓其飞,彭云建.变时滞模糊随机细胞神经网络新的鲁棒稳定性[J].控制与决策,2011,26(8):1197-1202.
[9]BLYTHE S,MAO X Y.Stability of stochastic delay neural networks[J].Journal of the Franklin Institute,2001,338(4):481-495.
[10]CAO J D,WANG J.Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays[J].Neural Networks,2004,17(3):379-390.
[11]YANG T,YANG L B.The global stability of fuzzy cellular networks[J].IEEE Trans Circuits and Systems I,1996,43(10):880-883.
[2]ZHANG Q H,XING R G.Global asymptotic stability of fuzzy cellular neural networks with time-varying delays[J].Physics Letters A,2008,327(22):3971-3978.
[3]刘振伟,张化光,佟绍成.一类时变时滞模糊细胞神经网络的时滞依赖指数稳定性判据[J].电子学报,2009,37(3):513-518.
[4]WANG J,LU J G.Global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms[J].Chaos,Solitons and Fractals,2008,38(3):878-885.
[5]周凤燕.随机时滞反应扩散广义细胞神经网络的均值指数稳定性[J].数学的实践与认识,2012,42(3):168-179.
[6]张伟伟,王林山.S-分布时滞随机区间细胞神经网络的全局指数鲁棒稳定性[J].山东大学学报:理学版,2012,47(3):87-92.
[7]张千宏,杨利辉,刘璟忠.变时滞随机模糊细胞神经网络的均方指数稳定性分析[J].安徽大学学报:自然科学版,2013,37(1):13-17.
[8]李亚军,邓其飞,彭云建.变时滞模糊随机细胞神经网络新的鲁棒稳定性[J].控制与决策,2011,26(8):1197-1202.
[9]BLYTHE S,MAO X Y.Stability of stochastic delay neural networks[J].Journal of the Franklin Institute,2001,338(4):481-495.
[10]CAO J D,WANG J.Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays[J].Neural Networks,2004,17(3):379-390.
[11]YANG T,YANG L B.The global stability of fuzzy cellular networks[J].IEEE Trans Circuits and Systems I,1996,43(10):880-883.