We　deal　with　the　state　consensus　problem　of　a　general　Linear　Interconnected　Multi-Agent　System　(LIMAS)　under　a　time-invariant　and　directed　communication　topology.　Firstly,　we　propose　a　linear　consensus　protocol　in　a　general　form,　which　consists　of　state　feedback　of　the　agent　itself　and　feedback　form　of　the　relative　states　between　the　agent　and　its　neighbors.　Secondly,　a　state-linear-transformation　is　applied　to　equivalently　transform　the　state　consensus　problem　into　a　partial　stability　problem.　Based　on　the　partial　stability　theory,　we　derive　a　sufficient　and　necessary　criterion　of　consensus　convergence,　which　is　expressed　via　the　Hurwitz　stability　of　a　real　matrix　constructed　from　the　parameters　of　the　agent　models　and　the　protocols,　and　present　an　analytical　formula　of　the　consensus　function.　Lastly,　we　propose　a　design　procedure　of　the　gain　matrices　in　the　protocol　by　solving　a　bilinear　matrix　inequality.