Finite-Time Synchronization Control for Quaternion-Valued Memristive Neural Networks by Halanay Inequality

This paper investigates the finite-time synchronization (FTS) of quaternion-valued memristive neural networks (QVMNNs) with mixed time delays. Utilizing the Halanay inequality, the analysis of the FTS issue involves two crucial steps: the convergence of the error system from the initial state to the unit ball, and subsequently from the unit ball to the origin. This approach not only obviates the necessity for constructing intricate Lyapunov functionals but also simplifies the treatment of delay terms. Furthermore, to streamline the theoretical derivation process, the considered QVMNNs are addressed without any decomposition by introducing the 1-norm, 2-norm, and ∞norm of quaternions. Based on these considerations, a series of algebraic criteria for FTS is formulated, alongside estimates of synchronization time under different initial conditions. Finally, numerical simulations are presented to validate the effectiveness of the theoretical findings and demonstrate the application of OVMNNs in secure communication.