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For decreasing communication load and overcoming network constrains, such as the limited bandwidth and data loss in multi-agent networks, this paper integrates the two control strategies to investigate the bounded consensus problem of multi-agent systems (MASs) with external disturbance on the basis of an undirected graph, namely, the quantized control and the event-triggered control. In the existence of the external disturbance, two types of the high-gain control laws with the uniform quantized relative state measurements for the bounded consensus problem of MASs are first discussed, respectively. Then, in order to save the limited network resources in a multi-agent network, the event-triggered quantized communication protocols are designed based on the first case to obtain the bounded consensus in multi-agent systems. Moreover, it is shown that “Zeno behavior” phenomenon can be excluded under the two event-triggered quantized control mechanisms, and the boundness of the relative state error can be adjusted by selecting the different parameters. Finally, two examples are shown to validate the feasibility and efficiency of our theoretical analysis. [ABSTRACT FROM AUTHOR]