This paper investigates the stability of a class of fractional-order static neural networks. Two new Lyapunov functions with proper integral terms are constructed. These integrals with variable upper limit are convex functions. Based on the fractional-order Lyapunov direct method and some inequality skills, several novel stability sufficient conditions which ensure the global Mittag–Leffler stability of fractional-order projection neural networks (FPNNs) are presented in the forms of linear matrix inequalities (LMIs). Two LMI-based Mittag–Leffler stability criteria with less conservativeness are given for a special kind of FPNNs. Finally, the effectiveness of the proposed method is demonstrated via four numerical examples.

中文翻译：

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一类分数阶静态神经网络稳定性的新结果

本文研究了一类分数阶静态神经网络的稳定性。构造了两个具有适当积分项的新李雅普诺夫函数。这些具有可变上限的积分是凸函数。基于分数阶Lyapunov直接方法和一些不等式技巧，以线性矩阵不等式（LMI）的形式呈现了几个新的稳定性充分条件，这些条件确保分数阶投影神经网络（FPNN）的全局Mittag-Leffler稳定性。对于一种特殊的 FPNN，给出了两个保守性较低的基于 LMI 的 Mittag-Leffler 稳定性标准。最后，通过四个数值例子证明了所提出方法的有效性。