给出了延迟离散 Hopfield-型网络的收敛性定理 ,提出了用于组合优化计算的延迟扰动算法 .在正规异步运行规则下 ,证明了网络滞后于能量函数收敛的步数由 Hopfield结果的 n2 步降到 2 n +1步 .揭示了离散 Hopfield-型网络与延迟离散 Hopfield-型神经网络收敛性的内在关系 ,为离散Hopfield-型网络的应用研究构筑了新的框架 The convergence theorem of delayed discrete-time Hopfield-type networks is given and a delay perturbation algorithm is proposed for combinatorial optimization calculation. Under normal asynchronous operation rules, it is proved that the number of steps that the network lags behind the energy function converges is changed from n2 To 2 n +1 steps.It reveals the inherent relationship between the discrete Hopfield-type networks and the delay discrete Hopfield-type neural networks convergence, and establishes a new framework for the application of discrete Hopfield-type networks