This　paper　considers　the　stochastic　consensus　problem　of　high-order　linear　discrete-time　multiagent　systems　(MASs)　with　uncertain　topologies　and　external　disturbances.　The　randomly　switching　interaction　signed　topologies　are　governed　by　a　time-homogenous　Markov　chain　with　incomplete　knowledge　of　the　transition　probabilities.　Based　on　Lyapunov　function　theory　and　adaptive　control　strategies,　we　employ　a　homogeneous　parameter-dependent　Lyapunov　function　to　propose　sufficient　conditions　under　a　set　of　linear　matrix　inequality　(LMI)　constraints.　A　free-weighting　matrix　method　is　introduced　to　give　the　proposed　LMIs　extra　freedom　to　search　feasible　solutions.　Furthermore,　the　adaptive　controllers　applied　in　this　paper　are　independent　of　topologies　and　fully　distributed;　i.e.,　the　system　achieves　robust　consensus　without　continuously　updating　the　controller　and　dealing　with　global　data.　Additionally,　we　extend　the　theoretical　framework　to　analyze　the　disturbance　rejection　performance　of　MASs　under　the　stochastic　process.　Two　numerical　examples　are　provided　to　show　the　effectiveness　of　the　algorithms.　©　2021　Elsevier　B.V.