The　leader–following　consensus　of　linear　heterogeneous　multiagent　systems　is　investigated　in　this　paper.　To　comply　with　the　most　practical　scenario,　the　communicating　topologies　among　agents　are　assumed　to　switch　stochastically　and　driven　by　a　continuous-time　discrete-state　Markov　process,　whose　state　space　corresponds　to　all　the　possible　topologies.　A　novel　distributed　adaptive　compensator　is　designed　for　the　followers　to　reconstruct　the　exogenous　signals　without　knowing　the　Laplacian　matrix　who　is　regarded　as　a　global　information,　and　sufficient　conditions　are　given　to　ensure　the　compensator　converges　to　the　dynamic　of　the　leader　asymptotically　in　the　mean　square　sense.　Then,　based　on　the　compensator,　we　solved　the　consensus　problem　both　by　distributed　state　and　measurement　output　feedback　control　schemes　under　output　regulation　framework,　which　allow　followers　to　have　nonidentical　state　dimensions.　Finally,　the　theoretical　results　are　demonstrated　by　a　numerical　example.　©　2023　John　Wiley　&　Sons　Ltd.