Fixed-Time Synchronization of Complex-Valued Inertial Neural Networks via Nonreduced-Order Method

This article investigates the fixed-time synchronization problem of a class of delayed complex-valued inertial neural networks (CVINNs). The analysis does not rely on the traditional reduced-order transformation, but constructing Lyapunov functions directly focused on the original system. Based on the direct method and the separation method, different control strategies are proposed, under which the addressed CVINNs can achieve synchronization perfectly in a fixed time. The corresponding synchronization criteria in terms of matrix inequalities are derived, which are more concise and easier to verify than algebraic inequalities conditions, and the estimation of the settling times. The direct method makes full use of some innovative inequalities in the complex field; the exponential parameters in the designed controllers are independent. Finally, in order to fully support the theoretical results, based on two typical activation functions, the proposed theoretical results are numerically validated and compared.