This　study　presents　a　distributed　observer-based　H　infinity　consensus　control　for　general　linear　multi-agent　systems　under　measurement　noises　and　external　disturbances.　By　using　the　state　linear　transformation　with　the　matrix　constructed　from　the　incidence　matrix　of　a　virtual　chained　directed　spanning　tree,　we　transform　the　observer-based　consensus　problem　into　an　asymptotic　stability　problem　of　a　corresponding　augmented　linear　system.　The　augmented　linear　system　consists　of　the　reduced-order　system　deduced　from　dynamic　equations　of　the　agents　and　state　estimation　error　system.　Based　on　asymptotic　stability　of　the　augmented　linear　system,　we　present　some　sufficient　conditions　in　terms　of　linear　matrix　inequalities　for　the　existence　of　the　distributed　observer-based　H　infinity　consensus　controller.　Finally,　the　effectiveness　of　the　proposed　approach　is　illustrated　by　a　numerical　example.