Consensus　problem　was　studied　for　continuous-time　linear　high-order　multi-agent　system　with　time-varying　delay　under　multi-type　switching　communication　topologies　under　the　case　that　the　system　switches　between　consensusable　and　unconsensusable　communication　topologies.　This　consensus　problem　was　equivalently　transformed　into　an　asymptotic　stability　problem　of　a　corresponding　switched　delay　system　by　a　linear　transformation.　Based　on　the　stability　theory　of　the　switched　systems　and　time-delay　systems,　a　sufficient　condition　was　presented　by　the　average　dwell-time　method　in　terms　of　linear　matrix　inequalities　(LMIs)　to　guarantee　the　consensus　of　the　multi-agent　system.　The　simulation　result　illustrates　the　effectiveness　of　the　obtained　results.　©　2016,　Beijing　University　of　Technology.　All　right　reserved.