This　paper　mainly　investigates　periodic　event-triggered　consensus　problem　for　double-integrator　multiagent　system　over　a　fixed　weighted　directed　communication　topology.　Event-triggered　consensus　protocol　based　on　event　instants　is　designed　to　reduce　the　frequency　of　actuation　updating,　which　contains　different　gain　weights　for　different　double-integrators.　The　event-triggered　algorithms　under　periodic　communication　and　event-based　communication　are　designed,　respectively.　The　linear　transformation　and　S-procedure　methods　are　used　to　obtain　consensus　criteria　for　ensuring　the　asymptotic　state　consensus　of　the　multiagent　system.　Finally,　numeral　examples　are　given　to　illustrate　the　effectiveness　of　our　results.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.