For　the　digital　control　of　SAPF(Shunt　Active　Power　Filter),　the　Delta　operator　state-space　model　of　SAPF　is　built　based　on　the　compensation　principle,　which　regards　the　load　harmonic　current　as　disturbance　and　the　source　harmonic　current　as　the　expected　output　of　power　system.　Its　H∞　controller　is　designed　with　LMI(Linear　Matrix　Inequality)　method.　The　compensation　performance　of　the　designed　H∞　controller　is　compared　with　that　of　H∞　controller　based　on　traditional　Z　transformation.　Simulative　results　show　that　the　total　harmonic　distortion　of　SAPF　with　Delta　operator-based　H∞　controller　is　less　than　that　with　traditional　Z　transformation-based　H∞　controller.