变时滞细胞神经网络指数稳定性的一个判据

A Criterion of Exponential Stability of Cellular Neural Networks with Time-Varying Delay

利用同胚映射理论、向量Lyapunov函数思想、M矩阵理论和不等式技术,研究了具有变时滞的细胞神经网络模型的全局指数稳定性,给出了判定平衡点的存在唯一性以及全局指数稳定性的一个判据,并且估计了收敛速度指标.相比一些最近的文献,本文没有采用传统的Lyapunov泛函方法,并且也不需要输出函数在实数集上满足Lipschitz条件,这样就放宽了对网络的要求,使得获得的结果有更广的应用范围.最后的数值例子表明提供的判据不仅保守性小,而且计算简单.

This paper studies the exponential stability of cellular neural networks with time- varying delay by making use of the homoeomorphism theory, the idea of vector Lyapunov function, M- matrix theory and inequality - technique, offering the grounds for uniqueness of equilibrium point existence and the global exponential stability and estimating the exponential convergence rate index. Compared with some recent literatures, this paper neither uses the traditional Lipschitz function nor outputs the function collection to satisfy the Lipschitz condition, thus relaxing the requirements to the networks. The method of this paper is simple and valid for the stability analysis of the neural networks with time - varying delay. It is believed that these results are significant and useful for the design and applications of neural networks.