The　issue　of　non-fragile　controller＇s　designed　with　reachable　set　estimation　and　time-delay　for　multi-agent　systems(MASs)　is　investigated　in　this　paper.　The　information　interaction　among　agents　is　governed　by　a　set　of　switching　sequence,　which　can　be　described　by　continue-time　discrete　state　semi-Markov　process.　By　tree-transformation,　the　MASs　firstly　converted　into　reduced-order　system,　and　properly　considered　the　instability　of　the　parameters　with　the　dynamic　behavior　of　the　controller,　a　non-fragile　controller　is　designed　to　describe　the　system＇s　performance　cope　with　the　perturbation　from　the　con-troller.　The　sufficient　conditions　are　established　in　forms　of　a　series　of　linear　matrix　inequalities　which　are　based　on　Lyapunov-Krasovskii　method,　and　the　agent＇s　state　of　error　systems　is　bounded　by　a　finite　closed　set　will　be　guaranteed.　Finally,　the　availability　of　the　derived　theoretical　results　are　verified　by　two　numerical　simulations.&　COPY;　2023　The　Franklin　Institute.　Published　by　Elsevier　Inc.　All　rights　reserved.