To　address　the　difficulty　of　controlling　the　dynamic　stability　of　the　system　after　time-varying　delay　of　the　plate　thickness　detection　at　the　final　stand　of　the　hot　strip　finishing　mill.　Firstly,　a　T-S　fuzzy　model　based　on　rolling　force　and　thickness　state　is　established　for　the　final　stand　of　the　hot　strip　finishing　mill,　and　the　maximum　time　delay　for　plate　thickness　detection　is　divided　into　several　time　delay　intervals　to　establish　a　linear　constant　state　space　model　of　the　time　delay　subintervals.　Secondly,　a　distributed　state　feedback　controller　satisfying　sufficient　conditions　for　stability　is　solved　by　using　the　parallel　distribution　compensation　(PDC)　principle　combined　with　Lyapunov　stability　theory　and　linear　matrix　inequality　(LMI)　methods.　Simulation　comparisons　with　current　M-AGC　and　Smith　prediction　M-AGC　system　(Smith-AGC)　show　that　our　method　can　effectively　reduce　overshoot　and　oscillations　in　the　dynamic　response　of　the　exit　plate　thickness　when　the　operating　conditions　change　and　the　system　time　delay　parameters　are　mismatched,　so　that　the　system　has　better　stability　and　dynamic　performance.