Global Mittag-Leffler projective synchronization for fractional-order neural networks: an LMI-based approach

*Correspondence: [email protected]; [email protected] 1Department of Applied Mathematics, Yanshan University, Qinhuangdao, 066001, China Full list of author information is available at the end of the article Abstract This paper is concerned with the global projective synchronization issue for fractional neural networks in the Mittag-Leffler stability sense. Firstly, a fractional-order differential inequality in the existing literature for the Caputo fractional derivative, with 0 < α < 1, is improved, which plays a central role in the synchronization analysis. Secondly, hybrid control strategies are designed via combing open loop control and adaptive control, and unknown control parameters are determined by the adaptive fractional updated laws to achieve global projective synchronization. In addition, applying the fractional Lyapunov approach and Mittag-Leffler function, the projective synchronization conditions are addressed in terms of linear matrix inequalities (LMIs) to ensure the synchronization. Finally, two examples are given to demonstrate the validity of the proposed method.