LMI-based criterion for global Mittag-Leffler lag quasi-synchronization of fractional-order memristor-based neural networks via linear feedback pinning control

Abstract

This paper addresses global Mittag-Leffler lag quasi-synchronization (GMLQS) of fractional-order memristor-based neural networks (FMNNs). Firstly, for a general class of fractional-order nonlinear systems with interval uncertainties, a kind of linear feedback pinning controller, which works by feeding back partial state errors to the partial controlled variables, is designed to achieve global Mittag-Leffler ultimate boundedness (GMUB). Correspondingly, a GMUB criterion in the form of linear matrix inequality (LMI) is derived with the aid of a Lyapunov function and a newly established fractional-order differential inequality. Then, the linear feedback pinning controller is employed for GMUB of the synchronization error system, which is equivalent to GMLQS of FMNNs. Since there exists the propagation delay between drive-response FMNNs and the synchronization error system can not be obtained straightforwardly, an identical equation about Caputo’s fractional derivatives is established to overcome this difficulty. Moreover, the detailed pinning control scheme design procedures for a prescribed GMLQS performance are presented, where the performance involves both ultimate error bound and transient behavior. In the control scheme, an auxiliary LMI and an optimization objective function are introduced, which can significantly reduce control cost. Finally, a numerical example is presented to show the feasibility of the control scheme. The results obtained in this paper have improved the existing criterion on quasi-synchronization of FMNNs, and will also provide a novel insight into pinning control of fractional-order nonlinear systems.