This research addresses the synchronization of delayed fractional-order memristive neural networks (DFMNNs) via quantized control. The motivations are twofold: (1) the transmitted information may be constrained by limited bandwidths; (2) the existing analysis techniques are difficult to establish LMI-based synchronization criteria for DFMNNs within a networked control environment. To overcome these difficulties, the logarithmic quantization is adopted to design two types of energy-saving and cost-effective quantized controllers. Then, under the framework of sector bound approach, the closed-loop drive-response DFMNNs can be represented as an interval system with uncertain feedback gains. By utilizing appropriate fractional-order Lyapunov functional and some inequality techniques, two LMI-based synchronization criteria for DFMNNs are derived to establish the relationship between the feedback gain and the quantization parameter. Finally, two illustrative examples are presented to validate the effectiveness of the proposed control schemes.

中文翻译：

---

延迟分数阶忆阻神经网络同步的量化控制

本研究通过量化控制解决了延迟分数阶忆阻神经网络（DFMNN）的同步问题。其动机是双重的：（1）传输的信息可能受到有限带宽的限制；（2）现有的分析技术很难在网络控制环境中为DFMNN建立基于LMI的同步标准。为了克服这些困难，采用对数量化来设计两种节能和具有成本效益的量化控制器。然后，在扇形边界方法的框架下，闭环驱动响应DFMNN可以表示为具有不确定反馈增益的间隔系统。通过利用适当的分数阶Lyapunov函数和一些不等式技术，推导了DFMNN的两个基于LMI的同步标准，以建立反馈增益与量化参数之间的关系。最后，给出了两个说明性的例子来验证所提出的控制方案的有效性。