Stability analysis of discrete-time recurrent neural networks based on standard neural network models
Stability analysis of discrete-time recurrent neural networks based on standard neural network models
复制标题
基于标准神经网络模型的离散时间递归神经网络稳定性分析
DOI：
10.1007/s00521-008-0211-5
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发表时间：
2009-11-01
影响因子：
6
通讯作者：
Liu, Meiqin
中科院分区：
文献类型：
--
作者：
Liu, Meiqin
为了方便地分析各种离散递归神经网络（RNN）的稳定性，包括双向联想记忆、Hopfield、细胞神经网络、Cohen-Grossberg神经网络和递归多层感知器等，提出了一种新的神经网络模型--标准神经网络模型（SNNM）来描述这类离散时间RNN。SNNM是一个线性动态系统和一个有界静态非线性算子的互连。将李雅普诺夫泛函与S-过程相结合，得到了离散时间SNNM的全局渐近稳定性判据，并将其条件表示为线性矩阵不等式。大多数延迟（或非延迟）的RNN可以转换为SNNM以统一的方式进行稳定性分析。SNNM在离散时间RNN稳定性分析中的一些应用实例表明，SNNM使RNN的稳定性条件易于验证。
In order to conveniently analyze the stability of various discrete-time recurrent neural networks (RNNs), including bidirectional associative memory, Hopfield, cellular neural network, Cohen-Grossberg neural network, and recurrent multiplayer perceptrons, etc., the novel neural network model, named standard neural network model (SNNM) is advanced to describe this class of discrete-time RNNs. The SNNM is the interconnection of a linear dynamic system and a bounded static nonlinear operator. By combining Lyapunov functional with S-Procedure, some useful criteria of global asymptotic stability for the discrete-time SNNMs are derived, whose conditions are formulated as linear matrix inequalities. Most delayed (or non-delayed) RNNs can be transformed into the SNNMs to be stability analyzed in a unified way. Some application examples of the SNNMs to the stability analysis of the discrete-time RNNs shows that the SNNMs make the stability conditions of the RNNs easily verified.