This　paper　investigates　a　decentralized　design　approach　of　leader-following　consensus　protocols　for　heterogeneous　multiagent　systems　under　a　fixed　communication　topology　with　a　directed　spanning　tree　(DST)　and　asymmetric　weight　matrix.　First,　a　control　protocol　using　only　the　information　of　the　neighbor　on　the　DST　of　each　agent　is　designed,　which　is　called　the　consensus　protocol　with　minimal　communication　links.　Particularly,　the　DST-based　linear　transformation　method　is　used　to　transform　the　consensus　problem　into　a　partial　variable　stability　problem　of　a　corresponding　system,　and　a　decentralized　design　method　is　proposed　to　find　the　gain　matrices　in　the　protocols.　Next,　the　decentralized　design　approach　is　extended　to　the　protocols　using　all　neighbor　information　in　the　original　communication　topology　with　the　help　of　the　matrix　diagonally　dominant　method.　Some　numerical　simulations　are　given　to　illustrate　the　theoretical　results.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2024.