Mittag-Leffler stabilization is studied for fractional reaction–diffusion cellular neural networks (FRDCNNs) in this paper. Different from previous literature, the FRDCNNs in this paper are high-dimensional systems, and boundary control and observed-based boundary control are both used to make FRDCNNs achieve Mittag-Leffler stability. First, a state-dependent boundary controller is designed when system states are available. By employing the spatial integral functional method and some inequalities, a criterion ensuring Mittag-Leffler stability of FRDCNNs is presented. Then, when the information of system states is not fully accessible, an observer is presented to estimate the system states based on boundary output and an observer-based boundary controller is provided aiming to stabilize the considered FRDCNNs. Furthermore, a robust observer-based boundary controller is proposed to ensure the Mittag-Leffler stability for FRDCNNs with uncertainties. Examples are given to illustrate the effectiveness of obtained theoretical results.

本文针对分数反应扩散细胞神经网络（FRDCNN）研究了Mittag-Leffler稳定性。与以前的文献不同，本文的FRDCNN是高维系统，边界控制和基于观测的边界控制都被用来使FRDCNN达到Mittag-Leffler稳定性。首先，当系统状态可用时，设计一个与状态有关的边界控制器。通过使用空间积分泛函方法和一些不等式，提出了确保FRDCNN的Mittag-Leffler稳定性的准则。然后，当无法完全访问系统状态的信息时，将提供一个观察者以基于边界输出来估计系统状态，并提供一个基于观察者的边界控制器以稳定考虑的FRDCNN。此外，提出了一种基于观测器的鲁棒边界控制器，以确保具有不确定性的FRDCNN的Mittag-Leffler稳定性。举例说明了所获得理论结果的有效性。