Finite-Time Synchronization of Reaction-Diffusion Inertial Memristive Neural Networks via Gain-Scheduled Pinning Control

For the considered reaction-diffusion inertial memristive neural networks (IMNNs), this article proposes a novel gain-scheduled generalized pinning control scheme, where three pinning control strategies are involved and
$2^{n}$
controller gains can be scheduled for different system parameters. Moreover, a time delay is considered in the controller to make it has a memory function. With the designed controller, drive-and-response systems can be synchronized within a finite-time interval. Note that the final finite-time synchronization criterion is obtained in the forms of linear matrix inequalities (LMIs) by introducing a memristor-dependent sign function into the controller and constructing a new Lyapunov–Krasovskii functional (LKF). Furthermore, by utilizing some improved integral inequality methods, the conservatism of the main results can be greatly reduced. Finally, three numerical examples are provided to illustrate the feasibility, superiority, and practicability of this article.