New fixed‐time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov‐Krasovskii functional method

Abstract

SummaryThe purpose of this article is to investigate the existence of periodic solutions and fixed‐time synchronization (FTS) of a class of discontinuous inertial neural networks (DINNs) with time‐varying delays. Due to the existence of the discontinuities, first, by using a generalized variable transformation, the original DINNs are transformed into a first‐order differential system. By using the differential inclusions theory and the set‐valued version of the Mawhin coincidence theorem, a new delay‐dependent criterion is derived to ensure the existence of periodic solutions. Furthermore, by designing some effective discontinuous control strategies and by constructing indefinite Lyapunov‐Krasovskii functional (LKF), algebraic criteria are derived to guarantee the FTS for the drive‐response system. The settling time is explicitly estimated. In comparison with the related results on INNs, it is the first time to study the existence result of the DINNs and the Lyapunov approaches applied to investigate the FTS are entirely different. Finally, the correctness of the main results is verified via numerical examples.