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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay
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Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay

机译：基于分数阶忆阻器的时滞神经网络的全局镇定

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This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.
机译：本文讨论了具有时滞的基于分数阶忆阻器的神经网络（FMNN）的全局稳定性。考虑电压阈值型忆阻器模型，FMNNs由具有不连续右手边的分数阶微分方程表示。然后，基于分数阶微分包含和集值映射，并借助Lyapunov函数和比较原理来解决该问题。设计了两种控制律（延迟状态反馈控制和耦合状态反馈控制）。因此，建立了两种类型的稳定标准[代数形式和线性矩阵不等式（LMI）形式]。延迟状态反馈控制中包括两组可调参数，可以对其进行灵活选择，以实现所需的全局渐近稳定或全局Mittag-Leffler稳定。由于现有的基于LMI的分数阶系统稳定性分析技术不适用于延迟的分数阶非线性系统，因此建立了分数阶微分不等式来克服这一困难。基于耦合状态反馈控制，借助新建立的分数阶微分不等式，首次开发了一些LMI稳定标准。所获得的LMI结果为延迟分数阶非线性系统的研究提供了新的见识。最后，给出了三个数值例子来说明所提出的理论结果的有效性。

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