This　paper　concentrates　on　the　robust　mean　square　consensus　problem　for　linear　continuous-time　multi-agent　systems　over　randomly　switching　topologies.　The　switching　process　is　governed　by　a　time-homogeneous　Markov　chain.　With　the　application　of　a　parameter　dependent　Lyapunov　functions　method,　the　sufficient　condition　to　reach　mean　square　consensus　is　derived　under　a　control　protocol　by　solving　a　set　of　linear　matrix　inequalities.　Finally,　a　numerical　simulation　example　is　given　to　demonstrate　the　effectiveness　of　the　proposed　algorithm.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.