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Synchronization of quaternion‐valued coupled systems with time‐varying coupling via event‐triggered impulsive control

In this paper, the problem of exponential synchronization of quaternion‐valued coupled systems based on event‐triggered impulsive control is investigated for the first time. It should be pointed out that the coupling strength is quaternion‐valued and time‐varying, which makes our model more in line with practical models. First, we prove that event‐triggered impulsive control can exclude Zeno behavior. Then, based on the Lyapunov method and the graph theory, some sufficient conditions are derived to ensure that quaternion‐valued coupled systems reach synchronization. Furthermore, as an application of our theoretical results, exponential synchronization of quaternion‐valued Kuramoto oscillators is studied in detail and a synchronization criterion is presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.