连续BAM神经网络的稳定性分析—LMI/BMI方法

Stability analysis of continuous time BAM neural networks: an LMI/BMI approach

对于连续双向联想记忆(BAM)神经网络的平衡点的稳定性问题,目前人们已经得到了很多富有意义的成果。本文提出一种新的神经网络模型-标准神经网络模型(SNNM),利用不同的Lyapunov泛函和S方法推导出基于线性/双线性矩阵不等式(LMI/BMI)的SNNM全局渐近稳定性和全局指数稳定性的充分条件。通过状态的线性变换,将连续BAM神经网络转化为SNNM,并利用有关SNNM的稳定性的一些结论,得到连续BAM神经网络平衡点的全局渐近稳定性和全局指数稳定性的充分条件,这些条件都以LMI或BMI形式给出,容易验证,保守性低。该方法扩展了以前的稳定性结果,同时也适用于其它类型的递归神经网络的稳定性分析。

So far many fruitful results have been obtained for stability of equilibrium points of continuous time bidirectional associative memory (BAM) neural network. A novel neural network model termed standard neural network model (SNNM) was advanced. By combining a number of different Lyapunov functional with S-procedure, some useful linear/bilinear matrix inequality (LMI/BMI)-based criteria for the global asymptotic stability and global exponential stability of the SNNM were derived. By using state affine transformation, the BAM neural networks were converted to the SNNMs. Based on some results of the SNNMs’ stability, some sufficient conditions for the global asymptotic stability and global exponential stability of the continuous time BAM neural networks were obtained, which were formulated as easily verifiable LMIs or BMIs, whose conservativeness is relatively low. The proposed approach improves the known stability results, and can also be applied to other forms of recurrent neural networks.