The Robust Stability Analysis Of Neural Networks With Time-varying Delays

In this paper, the existence, uniqueness and robust stability of three types of neural networks with time delays are considered, such as, the Hopfield neural networks, the shunting inhibitory cellular neural networks and Cohen-Grossberg neural networks. Some sufficient conditions for robust stability are given.The main works are illustrated as follows:First, without assuming the boundedness of the activation functions, the existence and uniqueness of the equilibrium point are proved by using homeomorphism techniques. And then, some sufficient conditions ensuring the global robust exponential stability and asymptotic stability of the equilibrium point for Hopfield neural network with continuous delay are derived by the Lyapunov stability theory. Comparisons between our results and previous results admit that our results establish a new set of stability criteria. Some examples are given to illustrate the effectiveness of our results.Second, the shunting inhibitory cellular neural networks with continuously distributed delays are considered. By employing fixed point theorem and differential inequality techniques, we have proved the existence and uniqueness of the almost periodic solutions. Sufficient conditions for the global exponential stability of the almost periodic solutions are established by using Lyapunov functional method. Now, few people considered the robust stability of the shunting inhibitory cellular neural networks, so this paper has a new result about it. An example is given to illustrate the effectiveness of our results.Third, we have considered the problem of robust exponential stability of Cohen-Grossberg neural networks with time-varying delays. Without assuming the boundedness and differentiability of the activation functions and the intervalizing of the coefficients of the system but using matrix to represent the perturbations, some sufficient conditions for the existence, uniqueness and global robust exponential stability of the equilibrium point are derived by the Lyapunov stability theory and linear matrix inequality (LMI) technique. Comparisons between our results and previous results admit that our results establish a new set of stability criteria. Some examples are given to illustrate the effectiveness of our results.