Further results on Mittag-Leffler synchronization of fractional-order coupled neural networks

• Main Authors: Fengxian Wang, Fang Wang, Xinge Liu
• Format: Article
• Language: English
• Published: SpringerOpen 2021-05-01
• Series: Advances in Difference Equations
• Subjects: Fractional-order coupled neural networks; Synchronization; LMIs
• Online Access: https://doi.org/10.1186/s13662-021-03389-7

Abstract In this paper, we focus on the synchronization of fractional-order coupled neural networks (FCNNs). First, by taking information on activation functions into account, we construct a convex Lur’e–Postnikov Lyapunov function. Based on the convex Lyapunov function and a general convex quadratic function, we derive a novel Mittag-Leffler synchronization criterion for the FCNNs with symmetrical coupled matrix in the form of linear matrix inequalities (LMIs). Then we present a robust Mittag-Leffler synchronization criterion for the FCNNs with uncertain parameters. These two Mittag-Leffler synchronization criteria can be solved easily by LMI tools in Matlab. Moreover, we present a novel Lyapunov synchronization criterion for the FCNNs with unsymmetrical coupled matrix in the form of LMIs, which can be easily solved by YALMIP tools in Matlab. The feasibilities of the criteria obtained in this paper are shown by four numerical examples.