Robust　H∞　consensus　control　of　multi-agent　systems　with　the　event-triggered　scheme　and　semi-Markov　switching　topologies　with　partially　unknown　rates　is　investigated　in　this　paper　to　suppress　system　uncertainty　and　external　disturbance.　By　defining　the　error　variable,　the　consensus　problem　is　firstly　converted　to　the　stability　problem　of　the　error　system.　A　sampling-data　event-triggered　protocol　is　introduced　to　avoid　the　continuous　communication　between　agents　and　co-design　the　gain　of　consensus　controller　and　the　event-triggered　parameters　matrix.　The　external　disturbance　is　considered　by　both　the　leader　and　follower,　the　sufficient　conditions　are　presented　to　guarantee　the　H∞　performance　in　accordance　with　linear　matrix　inequalities.　Finally,　the　suppression　of　external　input　disturbance　using　the　proposed　method　is　verified　by　a　numerical　example.　©　2022　IEEE.