This　paper　investigates　the　formation　problem　for　high-order　continuous-time　multi-agent　systems　with　time-varying　delay　under　switching　communication　topologies.　The　communication　topology　of　multi-agent　systems　switches　within　a　finite　set　of　digraphs　which　depicts　the　communication　structure　between　agents.　One　case　of　topology　set　is　considered:　there　does　not　exist　a　directed　spanning　tree　for　each　of　the　topologies　but　there　exists　a　directed　spanning　tree　for　the　union　of　all　the　topologies.　By　a　linear　transformation,　the　formation　problem　is　transformed　into　stability　analysis　of　a　switched　delay　systems.　With　the　help　of　a　stabilizing　switching　law,　sufficient　conditions　for　multi-agent　systems　to　achieve　a　given　formation　under　switching　topologies　are　presented　in　terms　of　linear　matrix　inequalities　(LMIs).　A　formation　example　of　intelligent　vehicle　system　is　shown　to　illustrate　the　effectiveness　of　the　switching　strategies.　©　2016　TCCT.