This　paper　studies　the　formation　control　problem　of　heterogeneous　linear　multi-agent　systems　(MASs)　with　time-invariant　relative　position　and　angle　constraints　under　a　directed　fixed　communication　topology.　A　consensus-based　formation　control　protocol　is　proposed　for　the　MAS　based　on　the　local　information　exchange　between　agents.　First,　we　transform　the　formation　control　problem　into　the　consensus　problem.　Then,　the　state　linear　transformation　approach　is　used　to　further　transform　the　consensus　problem　into　the　partial　variable　stability　problem.　Using　the　theory　of　partial　variable　stability,　sufficient　and　necessary　criteria　are　given　to　ensure　the　MAS　realizes　the　required　formation.　In　addition,　the　design　process　of　the　gain　matrices　in　control　protocol　is　given　based　on　Lyapunov　inequality　and　bilinear　matrix　inequality　(BMI).　Finally,　a　simulation　example　is　presented　to　illustrate　the　validity　of　the　theoretical　results.　©　2021　IEEE