Global Ultimate Mittag-Leffler Lag Quasi-Synchronization of Delayed Fractional-Order Memristive Neural Networks with Switching Jumps Mismatch via Pinning Control
Jia Jia, Zhigang Zeng · 2020
In this paper, a novel pinning controller, which is applied to the selected partial neurons with partial errors needed, is designed for global ultimate Mittag-Leffler lag quasi-synchronization (GUMLQS) of delayed fractional-order memristive neural networks (FMNNs) with switching jumps mismatch. Since the right-hand sides of the equations of FMNNs are discontinuous, FMNNs have no solution in the ordinary sense, and Filippov solutions are adopted for FMNNs. With the assistance of fractional Halanay inequality, a Lyapunov function in quadratic form and the theory of fractional derivative, an LMI-based GUMLQS criterion is derived. For a prescribed GUMLQS error bound, the control gain matrices can be calculated out via a group of LMIs. Meanwhile, the sufficient condition for the feasibility of the LMIs is obtained, which is an important basis for the selection of controlled neurons. Finally, a numerical example shows that the designed pinning controller can achieve GUMLQS between master-slave FMNNs with the prescribed ultimate error bound.