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In this study, a novel distributed event‐triggered scheme (ETS) using only triggered information is presented to solve the problem of the leader‐following consensus for a class of multi‐agent systems with general linear dynamics under fixed and switching topologies. First, the novel triggering conditions are proposed for fixed topology by virtue of discrete communications between neighbouring agents at the triggering times, which eliminates continuous inter‐agent communication and reduces the frequency of controller update simultaneously. Second, for switching topology including both graphs that have directed spanning tree and graphs that do not, the authors propose the topology‐dependent distributed ETS to guarantee consensus by an average dwell time approach. Noteworthily, Zeno behaviour of triggering time sequences is excluded under fixed and switching topologies. Examples validate the effectiveness and show the advantage of the proposed ETS by comparison. [ABSTRACT FROM AUTHOR]