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The consensus problem for multi-agent systems with general linear node dynamics and a fixed directed topology is investigated in this paper. Unlike existing linear multi-agent system models, the information transmission between neighboring agents are assumed to be intermittent in the present framework. To achieve consensus, a new class of distributed protocols are designed. By using tools from matrix analysis and switching systems theory, it is shown that this consensus problem can be cast to the stability problem of a set of low-dimensional switching systems. It is then proved that there exists a protocol guaranteeing consensus if the communication rate is larger than a threshold value and the communication topology contains a directed spanning tree. At last, a multi-step intermittent consensus protocol design procedure is provided for constructing such a protocol.