Abstract

This paper is concerned with the generalized finite-time stability, boundedness and stabilization for fractional-order memristive neural networks (FMNNs) with the fractional-order 0 < α < 1. Under the fractional-order Filippov differential inclusion frame, FMNNs are modelled as a fractional-order differential equation with discontinuous right-hand. Based on the topological degree property, the existence of equilibrium point of FMNNs is proved. By means of the generalized Gronwall inequality, the Laplace transform and the Lyapunov functional candidate, some conditions to guarantee the generalized finite-time stability and boundedness for FMNNs are derived in terms of linear matrix inequalities (LMIs). In addition, by using appropriate feedback controller, the generalized finite-time stabilization condition is also addressed in forms of LMIs. Finally, two examples are given to demonstrate the validity of the theoretical results.

中文翻译：

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分数阶忆阻神经网络的广义有限时间稳定性和镇定

摘要

本文关注分数阶0 <α<1的分数阶忆阻神经网络（FMNN）的广义有限时间稳定性，有界性和稳定性。在分数阶Filippov微分包含框架下，将FMNN建模为右手不连续的分数阶微分方程。基于拓扑度的性质，证明了FMNNs平衡点的存在。借助于广义Gronwall不等式，Laplace变换和Lyapunov函数候选，根据线性矩阵不等式（LMI）得出了保证FMNN的广义有限时间稳定性和有界性的一些条件。另外，通过使用适当的反馈控制器，还可以以LMI的形式解决广义的有限时间稳定条件。