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The event-triggered consensus of multi-agent systems received extensive attention in academia and industry perspectives since it ensures all agents eventually converge to a stable state while reducing the utilization of network communication resources effectively. However, the practical limitation of the actuator could lead to a saturation phenomenon, which may degrade the systems or even induce instability. This paper plans to offer a detailed review of some recent results in the event-triggered consensus of multi-agent systems subject to actuator saturation. First, the multi-agent system model with actuator saturation constraints is given, and the basic framework of the event-triggering mechanism is introduced. Second, representative results reported in recent valuable papers are reviewed based on methods for dealing with saturated terms, including low-gain feedback, sector-bounded conditions, and convex hull representations. Finally, some challenging topics worthy of research efforts are dicussed for future research.

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