Considering　that　the　controller　parameters　are　of　additive　norm-bounded　uncertainties　when　realized,　a　design　method　of　robust　non-fragile　H-infinity　controller　for　uncertain　system　based　on　Delta　operator　theory　is　illustrated　in　this　paper.　A　sufficient　and　necessary　condition　of　the　existence　for　the　controller　is　given,　which　is　presented　in　LMI　forms.　Finally,　the　designed　method　is　used　in　the　speed　control　system　of　permanent　magnet　linear　synchronous　motor　(PMLSM).　With　the　designed　controller,　the　resulted　speed　closed-loop　system　is　still　stable　and　has　the　expected　H-infinity　performance　even　if　the　sample　period　is　reduced　and　the　parameters　of　the　controller　and　the　controlled　object　are　of　variations.　The　results　show　that　the　designed　method　is　effective.　©　2007　Editorial　Board　of　Control　Theory　&　Applications.