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In the proposed protocol, agents in multi-agent systems update controllers by utilizing estimated state values in the triggered intervals. And for reducing the burdens of bandwidth further, the model-based event-triggered protocol is extended to self-triggered protocol which does not need continuous communication in triggered intervals. It is proven that Zeno behavior is excluded. Our main contributions are giving a novel distributed model-based event-triggered protocol for fixed-time consensus and extending it into a self-triggered protocol. 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