Zhang Huaguang, Liu Zhenwei, Huang Guang-Bin, Wang Zhanshan
School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, China.
IEEE Trans Neural Netw. 2010 Jan;21(1):91-106. doi: 10.1109/TNN.2009.2034742. Epub 2009 Dec 4.
In this paper, a weighting-delay-based method is developed for the study of the stability problem of a class of recurrent neural networks (RNNs) with time-varying delay. Different from previous results, the delay interval [0, d(t)] is divided into some variable subintervals by employing weighting delays. Thus, new delay-dependent stability criteria for RNNs with time-varying delay are derived by applying this weighting-delay method, which are less conservative than previous results. The proposed stability criteria depend on the positions of weighting delays in the interval [0, d(t)] , which can be denoted by the weighting-delay parameters. Different weighting-delay parameters lead to different stability margins for a given system. Thus, a solution based on optimization methods is further given to calculate the optimal weighting-delay parameters. Several examples are provided to verify the effectiveness of the proposed criteria.
本文提出了一种基于加权延迟的方法，用于研究一类具有时变延迟的递归神经网络（RNN）的稳定性问题。与先前的结果不同，通过采用加权延迟将延迟区间[0, d(t)]划分为一些可变子区间。因此，应用这种加权延迟方法推导了具有时变延迟的RNN的新的时滞依赖稳定性准则，这些准则比先前的结果保守性更低。所提出的稳定性准则取决于加权延迟在区间[0, d(t)]中的位置，其可以由加权延迟参数表示。对于给定系统，不同的加权延迟参数导致不同的稳定裕度。因此，进一步给出了一种基于优化方法的解决方案来计算最优加权延迟参数。提供了几个例子来验证所提出准则的有效性。
