一类具多比例时滞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泛函和运用Halanay时滞不等式,讨论一类具多比例时滞细胞神经网络的全局指数稳定性,得到了判定该系统平衡点全局指数稳定的一个时滞独立的充分条件.通过数值算例和仿真结果验证了所得结论的有效性.
Global exponential stability of a class of cellular neural networks with multi-proportional delays is studied. The sufficient conditions of global exponential stability of the equilibrium of system are obtained by constructing suitable Lyapunov functional and Halanay delay inequality. An example is given to illustrate the effectiveness of the result.
Global exponential stability of a class of cellular neural networks with multi-proportional delays is studied. The sufficient conditions of global exponential stability of the equilibrium of system are obtained by constructing suitable Lyapunov functional and Halanay delay inequality. An example is given to illustrate the effectiveness of the result.
引文
[1]CHUA L O,YANG L.Cellular neural network:theory and applications[J].IEEE Trans CAS,1988,35(10):1257-1290.
[2]程晓华,张国东.一类时滞细胞神经网络的稳定性分析[J].湖北师范学院学报:自然科学版,2010,30(3):32-35.
[3]马成荣.高阶S-分布时滞广义细胞神经网络的全局指数稳定性[J].生物数学学报,2011,26(3):459-468.
[4]张若军,王林山.具有分布时滞的细胞神经网络的概周期解[J].数学物理学报,2012,31(2):422-429.
[5]杨逢建,张超龙,吴东庆,等.具有时滞的一般型脉冲神经网络的指数稳定性[J].纯粹数学与应用数学,2011,27(1):1-6.
[6]LIU J.Global exponential stability of cellular neural networks with time-varying delays[J].Math Pract Theory,2009,39(15):194-199.
[7]莫玉忠,丁明智,虞继敏.变时滞非线性细胞神经网络稳定性分析[J].重庆邮电大学学报:自然科学版,2010,22(6):817-822.
[8]罗日才,许弘雷.一类中立型时滞神经网络的全局渐近稳定性[J].计算机工程与应用,2012,48(6):30-32.
[9]宫大为,冯建,刘金海.带有不确定的时变时滞神经网络渐近稳定性分析[J].东北大学学报:自然科学版,2010,31(3):313-316.
[10]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.
[11]KAO Y G,GAO C C,HAN W.Global exponential robust stability of reaction-diffusion interval neural networks with continuously distributed delays[J].Neural Computing and Applications,2010,19(6):867-873.
[12]CHEN H B,ZHANG Y,HU P.Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks[J].Neural Computing,2010,73(13):2554-2561.
[13]张迎迎,周立群.一类具多比例时滞的细胞神经网络的指数稳定性[J].电子学报,2012,40(6):1159-1163.
[14]周立群.多比例时滞的细胞神经网络的指数周期性与稳定性[J].生物数学学报,2012,27(3):480-488.
[15]ZHOU L Q.Delay-dependent exponential stability of cellular neural net-works with multi-proportional delays[J].Neural Process Letters,DOI 10.1007/s11063-012-9271-8.
[2]程晓华,张国东.一类时滞细胞神经网络的稳定性分析[J].湖北师范学院学报:自然科学版,2010,30(3):32-35.
[3]马成荣.高阶S-分布时滞广义细胞神经网络的全局指数稳定性[J].生物数学学报,2011,26(3):459-468.
[4]张若军,王林山.具有分布时滞的细胞神经网络的概周期解[J].数学物理学报,2012,31(2):422-429.
[5]杨逢建,张超龙,吴东庆,等.具有时滞的一般型脉冲神经网络的指数稳定性[J].纯粹数学与应用数学,2011,27(1):1-6.
[6]LIU J.Global exponential stability of cellular neural networks with time-varying delays[J].Math Pract Theory,2009,39(15):194-199.
[7]莫玉忠,丁明智,虞继敏.变时滞非线性细胞神经网络稳定性分析[J].重庆邮电大学学报:自然科学版,2010,22(6):817-822.
[8]罗日才,许弘雷.一类中立型时滞神经网络的全局渐近稳定性[J].计算机工程与应用,2012,48(6):30-32.
[9]宫大为,冯建,刘金海.带有不确定的时变时滞神经网络渐近稳定性分析[J].东北大学学报:自然科学版,2010,31(3):313-316.
[10]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.
[11]KAO Y G,GAO C C,HAN W.Global exponential robust stability of reaction-diffusion interval neural networks with continuously distributed delays[J].Neural Computing and Applications,2010,19(6):867-873.
[12]CHEN H B,ZHANG Y,HU P.Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks[J].Neural Computing,2010,73(13):2554-2561.
[13]张迎迎,周立群.一类具多比例时滞的细胞神经网络的指数稳定性[J].电子学报,2012,40(6):1159-1163.
[14]周立群.多比例时滞的细胞神经网络的指数周期性与稳定性[J].生物数学学报,2012,27(3):480-488.
[15]ZHOU L Q.Delay-dependent exponential stability of cellular neural net-works with multi-proportional delays[J].Neural Process Letters,DOI 10.1007/s11063-012-9271-8.