This　paper　investigates　the　consensus　problem　of　high-order　continuous-time　linear　multiagent　systems　(LMASs)　with　multitype　switching　topologies　which　include　both　consensusable　and　unconsensusable　communication　topologies.　A　linear　transformation　is　introduced,　which　equivalently　transforms　the　consensus　problem　into　the　stability　problem　of　a　corresponding　switched　system,　along　with　a　necessary　and　sufficient　condition　to　analyze　the　consensus　problem.　This　paper　is　aimed　at　studying　the　impact　of　a　switching　rule　on　communication　topologies　for　consensus　of　LMASs.　Based　on　the　dynamic　dwell　time　method,　a　sufficient　condition　is　derived　for　consensus　of　LMASs.　It　is　shown　that,　with　switching　signals　that　satisfy　this　switching　rule,　LMASs　can　achieve　consensus　under　directed　switching　communication　topologies.　A　numerical　example　is　provided　to　illustrate　the　effectiveness　of　the　theoretical　results.