The　paper　investigates　the　analysis　and　design　problem　of　state　consensus　via　dynamic　output　feedback　for　linear　Multi-Agent　Systems　(MASs)　under　a　time-invariant　directed　communication　topology.　First,　a　general　consensus　protocol　with　observers　is　adopted　using　the　estimated　state　of　the　agent　itself　and　the　relative　estimated　states　between　neighboring　agents.　Then　a　state-linear-transformation　is　proposed　to　transform　the　state　consensus　problem　into　a　partial　stability　problem.　Based　on　the　partial　stability　theory,　a　necessary　and　sufficient　criterion　for　state　consensus　is　deduced,　and　an　explicit　expression　of　the　state　consensus　function　is　given.　From　the　criterion,　a　procedure　to　design　gain　matrices　in　the　consensus　protocol　is　presented　by　applying　the　homotopy　method　to　solve　the　involved　Bilinear　Matrix　Inequality　(BMI).　Finally,　a　numerical　example　is　given　to　illustrate　the　effectiveness　of　theoretical　results.　(C)　2015　The　Franklin　Institute.　Published　by　Elsevier　Ltd.　All　rights　reserved.