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The main contribution is that a novel state-dependent intermittent scheme is proposed, where whether the control protocols are implemented on the agents or not is related to system dynamics. In this communication scheme, by dividing the nonnegative real region into three subregions, the work time and the rest time are dependent on the pre-given subregions and a function value describing the error state. Based on this, a novel state-dependent intermittent control protocol can be designed and the sufficient conditions for the overall consensus can further be obtained. Compared to the existing time-dependent intermittent communication schemes, the proposed state-dependent one can tolerate more rest time. 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