IEEE Trans Cybern. 2020 Oct;50(10):4281-4292. doi: 10.1109/TCYB.2019.2902864. Epub 2019 Mar 20.
This paper focuses on the dynamical behavior for a class of memristor-based bidirectional associative memory neural networks (BAMNNs) with additive time-varying delays in discrete-time case. The necessity of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is exponentially stable with a prescribed decay rate. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and utilizing Cauchy-Schwartz-based summation inequality, the delay-dependent sufficient conditions for the existence of the desired estimator are derived in the absence of uncertainties which are further extended to available uncertain parameters of the prescribed memristor-based BAMNNs in terms of linear matrix inequalities (LMIs). By solving the proposed LMI conditions the estimation gain matrices are obtained. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results.
本文针对离散时间情形下具有加性时变时滞的一类基于忆阻器的双向联想记忆神经网络（BAMNN）的动态行为进行了研究。提出该问题的必要性在于设计一个合适的状态估计器，使得相应的估计误差动力学在给定的衰减率下呈指数稳定。通过构造适当的李雅普诺夫-克拉索夫斯基泛函（LKF）并利用基于柯西-施瓦茨的求和不等式，在没有不确定性的情况下推导出了期望估计器存在的时滞相关充分条件，并进一步将其扩展到了给定基于忆阻器的 BAMNN 的可用不确定参数的情况下，形式为线性矩阵不等式（LMIs）。通过求解所提出的 LMI 条件，得到了估计增益矩阵。最后，通过两个数值例子说明了所提出的结果的有效性。
