This　study　focuses　on　the　consensus　problem　of　a　high-order　Linear　Multi-Agent　System　(LMAS)　with　directed　switching　information　topology.　After　introducing　the　notion　of　consensusable　information　topology　of　LMAS,　consensus　problem　is　considered　in　presence　of　a　topology　set　of　agents:　each　topology　in　the　set　is　consensusable.　By　a　proposed　linear　transformation,　we　investigate　the　consensus　problem　with　the　help　of　the　partial　stability　theory　of　a　corresponding　switched　system.　Sufficient　condition　is　derived　that　LMAS　can　achieve　consensus　by　the　trade-off　among　consensusable　topologies　in　terms　of　dynamic　dwell-time　conditions.　Numerical　example　is　provided　to　illustrate　the　effectiveness　of　the　proposed　method.