Event-Triggered Synchronization for Delayed Quaternion-Valued Inertial Fuzzy Neural Networks via Nonreduced Order Approach

This article mainly studies the synchronization problem for a class of Takagi–Sugeno (T–S) fuzzy quaternion-valued inertial neural networks with time-varying delay through event-triggered control (ETC) scheme. First, a class of quaternion-valued inertial fuzzy neural networks (QVIFNNs) model with time-varying delay is proposed. To avoid the increase of the number of state variables caused by reduced-order method, nonreduced order approach is utilized fully, and a fuzzy exponential gain event-triggered controller is designed so as to occupy the less communication resources. Then, by establishing a novel Lyapunov functional well handling the high-order term, a new synchronization condition is derived under static event-triggered scheme. And then, to further reduce the number of triggers, a dynamic event-triggered condition is developed and the corresponding sufficient criterion is given. Meanwhile, it is proved that the lower bound of event intervals are nonzero positive and the Zeno phenomenons do not exist via rigorous mathematical derivation. Finally, a numerical example is offered to show the effectiveness of the proposed method. An application example for the considered QVIFNNs with time-varying delay is given.