Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China.
Neural Netw. 2012 Jan;25(1):14-20. doi: 10.1016/j.neunet.2011.08.002. Epub 2011 Aug 22.
This paper investigates the problem of state estimation for Markovian jump Hopfield neural networks (MJHNNs) with discrete and distributed delays. The MJHNN model, whose neuron activation function and nonlinear perturbation of the measurement equation satisfy sector-bounded conditions, is first considered and it is more general than those models studied in the literature. An estimator that guarantees the mean-square exponential stability of the corresponding error state system is designed. Moreover, a mean-square exponential stability condition for MJHNNs with delays is presented. The results are dependent upon both discrete and distributed delays. More importantly, all of the model transformations, cross-terms bounding techniques and free additional matrix variables are avoided in the derivation, so the results obtained have less conservatism and simpler formulations than the existing ones. Numerical examples are given which demonstrate the validity of the theoretical results.
本文研究了具有离散和分布时滞的马尔可夫跳跃型 Hopfield 神经网络（MJHNN）的状态估计问题。首先考虑了神经元激活函数和测量方程的非线性摄动满足扇区有界条件的 MJHNN 模型，该模型比文献中研究的模型更为通用。设计了一个估计器，保证了相应误差状态系统的均方指数稳定性。此外，还给出了具有时滞的 MJHNN 的均方指数稳定性条件。这些结果取决于离散时滞和分布时滞。更重要的是，在推导过程中避免了所有的模型变换、交叉项上界技术和自由附加矩阵变量，因此得到的结果比现有结果具有更小的保守性和更简单的形式。给出了数值示例，验证了理论结果的有效性。
