This　paper　deals　with　the　problem　of　non-fragile　H.　controller　design　for　linear　time-invariant　systems　based　on　state　observers.　The　purpose　of　work　is　to　design　a　state　observer　and　a　memoryless　state　feedback　controller　such　that,　for　all　admissible　additive　observer　gain　variation　and　controller　gain　variation,　the　closed-loop　system　is　asymptotically　stable　and　has　an　H-infinity　disturbance　attenuation　bound　y　via　linear　matrix　inequality　(LMI).　A　numerical　example　shows　the　effectiveness　of　the　proposed　design　approach.