Finite-time and fixed-time stabilization of multiple memristive neural networks with nonlinear coupling.

Abstract

This brief presents the finite-time stabilization and fixed-time stabilization of multiple memristor-based neural networks (MMNNs) with nonlinear coupling. Under the retarded memristive theory, the generalized Lyapunov functional method, extended Filippov-framework and Laplacian matrix theory, we can realize both the finite-time stabilization and fixed-time stabilization problem of MMNNs by designing novel state-feedback controller and the corresponding adaptive controller with regulate parameters. Moreover, we assess the bounds of settling time for the both two kinds of stabilization respectively, and we deeply analyze the influence of initial desiring values and the linear growth condition of the controller on the system. Finally, the benefits of the proposed approach and the experimental analysis are demonstrated by numerical examples.