External　disturbances　can　render　constrained　multiagent　systems　(MASs)　unstable　and　affect　their　convergence　speed.　To　address　this　issue,　the　cooperative　control　strategy　for　MASs　based　on　a　predefined　time　(PT)　disturbance　observer　(PTDOB)　is　proposed　in　this　article.　First,　the　original　time-varying　constrained　states　of　MASs,　which　are　influenced　by　external　disturbances　and　have　a　coupled　communication　topology,　are　transformed　into　unconstrained　states　using　the　nonlinear　transformed　function　(NTF).　This　transformation　ensures　that　the　limitations　of　various　physical　states　for　agents　are　not　exceeded.　Second,　the　transformed　unconstrained　states　are　used　to　construct　the　PTDOB　for　fast　observation　of　external　disturbances.　Then,　based　on　the　proposed　PTDOB　and　the　backstepping　control　technique,　an　adaptive　fuzzy　PT　cooperative　controller　is　designed.　This　controller　not　only　ensures　the　convergence　of　MASs　within　PT　but　also　prevents　the　states　from　exceeding　the　time-varying　bounds.　Finally,　the　effectiveness　of　the　proposed　control　strategy　is　demonstrated　through　its　application　to　multiple　single-link　robotic　arms　as　illustrative　examples.