Stability Of Cellular Neural Networks With Delay

Since Hopfield put forward the neural networks models in 1982, applications of the famed Cellular Neural Networks have achieved notable development. It's necessary to induce delays, among cell when transmitting information in solving real problems. This is so called Delayed Cellular Neural Networks (DCNNs).Stability is a key issue in applications of cellular neural networks (CNNs). In some applications, it is desirable that the network possesses a unique and globally asymptotically stable equilibrium point for every external input. Because of uncertain facts in the models, the robust stability is very essential to some applications. The early literatures have shown that the research difficulty in Delayed Cellular Neural Networks is much more than non-delayed one. In this thesis, we choose a Lyapunov function to suit neural networks, through researching in theory of stability and neural networks, and then dispose the matrix with some skills. We get a better liner matrix inequality result, including global asymptotically stability, global exponential stability.In this paper, the study to this problem of global asymptotically stability and global exponential stability of Hopfield DCNNs, main four parts: (1)Apply Homeomorphism theorem, norm characteristic and LMI techniques, we obtained existence and uniqueness of the equilibrium point, and criterion of exponential stability, which contain one activation function; (2) Apply Lie algebra condition, inequality and integral approach, we obtained criterion of global asymptotically stability and exponential convergence estimate, which contain one activation function; (3)Apply norm characteristic, operation, and correlative lemmas, we obtained existence and uniqueness of the equilibrium point, and criterion of global exponential stability, which contain two activation function; (4)Via nonsmooth analysis and LMI approach, we obtained existence and uniqueness of the equilibrium point, and criterion of global asymptotically stability, which contain two activation function. Lastly, we present numerical examples to illustrate the effectiveness and utility of the results.