IEEE Trans Neural Netw Learn Syst. 2014 Nov;25(11):2099-109. doi: 10.1109/TNNLS.2014.2305440.
This paper presents new theoretical results on the passivity and passification of a class of memristor-based recurrent neural networks (MRNNs) with time-varying delays. The casual assumptions on the boundedness and Lipschitz continuity of neuronal activation functions are relaxed. By constructing appropriate Lyapunov-Krasovskii functionals and using the characteristic function technique, passivity conditions are cast in the form of linear matrix inequalities (LMIs), which can be checked numerically using an LMI toolbox. Based on these conditions, two procedures for designing passification controllers are proposed, which guarantee that MRNNs with time-varying delays are passive. Finally, two illustrative examples are presented to show the characteristics of the main results in detail.
本文提出了一类具有时变时滞的忆阻递归神经网络（MRNN）的被动性和被动化的新理论结果。放松了神经元激活函数有界性和 Lipschitz 连续性的因果假设。通过构造适当的 Lyapunov-Krasovskii 泛函并使用特征函数技术，将被动性条件表示为线性矩阵不等式（LMIs），可以使用 LMI 工具箱进行数值检查。基于这些条件，提出了两种设计被动化控制器的方法，保证了具有时变时滞的 MRNN 是被动的。最后，给出了两个实例来说明主要结果的特点。
