Based　on　LMI,　a　design　method　of　H∞　non-fragile　controller　for　Delta　operator　systems　which　feedback　gain　is　additive　uncertain　is　introduced.　A　sufficient　and　necessary　condition　is　given　such　that　the　resulted　closed-loop　Delta　operator　systems　are　stable　and　of　certain　H∞　performance.　The　certain　lemma　is　used　to　translate　the　resulted　sufficient　and　necessary　condition　into　linear　matrix　inequality　form.　A　numerical　example　shows　the　effectiveness　of　the　design　procedures.