This　paper　focuses　on　the　robust　mean-square　consensus　control　problem　for　linear　multiagent　systems　over　randomly　switching　signed　interaction　topologies.　The　stochastic　process　is　governed　by　a　time-homogeneous　Markov　chain　with　partly　unknown　transition　rates.　Sufficient　conditions　for　a　consensus　in　the　form　of　linear　matrix　inequalities　are　given　via　distributed　adaptive　control　based　on　parameter-dependent　Lyapunov　functions.　The　adaptive　control　protocols　require　only　the　neighbor　information　of　the　agents,　and　the　algorithm　that　designs　the　protocols　reduces　the　influence　of　the　communication　topology　on　the　consensus,　which　can　prevent　undesirable　interaction　impacts.　Moreover,　the　disturbance　rejection　problem　is　addressed　as　an　extension.　Finally,　two　simulations　are　utilized　to　illustrate　the　effectiveness　of　the　algorithms.　©　The　Author(s)　2021.