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In this study, the event-triggered average consensus control for discrete-time multi-agent systems (MASs) is investigated. Based on a Lyapunov function, a sufficient condition is derived to give an event condition, which is designed based on the measurement error and the disagreement vector. The sufficient condition, described in terms of a linear matrix inequality (LMI), is easily solved by available LMI toolbox. Under this event condition, the event-triggered MAS reaches average consensus. Furthermore, the results are extended to the self-triggered consensus control, where the next task release time can be decided depending on the current sampled data. In addition, a certain restriction on the event condition is proposed in order to avoid Zeno-behaviour. Finally, two simulation examples illustrate the effectiveness of the theoretical results.