This　paper　deals　with　the　problem　of　robust　and　non-fragile　H-infinity　control　via　state　feedback　for　a　class　of　linear　discrete-time　interval　systems.　The　non-fragile　controller　under　consideration　varies　in　an　unknown　interval,　but　its　offset　is　known.　The　sufficient　and　necessary　condition　for　the　existence　of　solutions　to　the　problem　is　presented　in　terms　of　linear　matrix　inequality　(LMI).　The　designed　controller　can　stabilize　the　closed-loop　systems　and　guarantee　a　prescribed　H-infinity　performance.　A　numerical　example　is　provided　to　demonstrate　the　validity　of　the　proposed　design　approach.