带时变时滞细胞神经网络的全局渐近稳定性

Global Asymptotic Stability of Cellular Neural Networks with Time-Varying Delays

研究了带时变时滞的细胞神经网络的全局渐近稳定性问题,给出了带时变时滞细胞神经网络平衡点全局渐近稳定的新充分判定准则。首先,提出所研究的时滞细胞神经网络模型、系统激活函数所需满足的条件及需要的引理。然后,将所研究的系统通过一个等式进行线性变换,在定义一个与系统相关的映射操作基础上,基于Lya-punov-Krasovskii稳定性定理和线性矩阵不等式技术来讨论时滞细胞神经网络的全局渐近稳定性。所得条件是时滞相关的。最后,用一个数值例子验证所得的稳定性条件是有效的。

The global asymptotic stability of cellular neural networks with time-varying delays is investigated. A novel sufficient judging criterion of the equilibrium point of global asymptotic stability of cellular neural networks with time-varying delays is given. First, the cellular neural network model with time-delay is proposed, the conditions for the system to acti- vate the function and the 1emma would be used are introduced. Then, the system under study carries out the ＂linearization＂ through an equation. The global asymptotic stability of cellular neural networks with time-delay is discussed by utilizing Lya- punov-Krasovskii functional method and the linear matrix inequality （LMI） technique, on the basis of defining a mapping operation system associated with the system. The results obtained are associated with the time-delay. Finally, a numerical example is given to verify the effectiveness of the proposed method.