In　this　paper,　we　study　the　consensus　problem　of　linear　multi-agent　systems　(LMAS)　in　directed　networks　with　switching　information　topology.　The　consensus　problem　is　transformed　into　the　partial　stability　problem　of　a　corresponding　auxiliary　system　by　a　linear　transformation.　For　a　pre-given　set　of　topologies,　We　address　two　cases:　1)　The　LMAS　achieves　the　consensus　under　each　fixed　information　topology　in　this　set;　2)　The　LMAS　achieves　the　consensus　under　some　information　topologies　in　this　set.　For　both　cases,　we　present　sufficient　conditions　that　sustain　the　consensus　of　the　LMAS　with　switching　topology　under　an　average　dwell　time　scheme,　respectively.　Simulation　results　are　also　given　to　demonstrate　the　effectiveness　of　the　theoretical　results.