中文摘要：

研究了离散时滞标准神经网络模型（SNNM）的鲁棒渐进稳定性和指数稳定性问题，结合Lyapunov稳定性理论和S方法推导出了两种稳定性的充分条件．所得到的稳定性条件被表示为线性矩阵不等式形式，便于求解．特别的，将鲁棒指数稳定性问题转化为一个广义特征值问题，除了可以判断网络的指数稳定性，还可以方便地估计其最大指数收敛率．在数值示例中，将两类递归神经网络（RNNs）转化为SNNM的形式并利用得到的相关结论对其鲁棒稳定性进行了分析，仿真结果验证了稳定性判据的有效性．SNNM为分析递归网络提供了新的思路，简单且有效．

英文摘要：

The problems of robust asymptotic stability and exponential stability of delayed discrete-time standard neural network model （SNNM） were investigated. Applying Lyapunov stability theory and S-procedure technique, sufficient stability conditions were derived in form of linear matrix inequalities, which could be solved easily. Especially, the condition for robust exponential stability was formulated as a generalized eigenvalued problem, which established an estimation of the exponential convergence rate and improved the previous results. In the given examples, two kinds of recurrent neural networks （RNNs） were transformed into SNNM to be analyzed in a unified way. Simulation showed the effectiveness of the presented method and the validity of the sufficient conditions. SNNM provides a new approach for the analysis of RNNs.