A　method　for　design　of　a　set-membership　filter　for　fault　diagnosis　of　a　nonlinear　system　with　unknown　but　bounded　faults　was　proposed　to　ensure　all　the　values　of　state　and　fault　signals　of　the　system　to　be　within　the　range　from　a　low　bound　to　an　upper　bound.　The　Takagi　Sugeno　(T-S)　fuzzy　model　was　employed　to　approximate　the　nonlinear　system,　with　the　assumption　that　the　values　of　process　noises,　measurement　noises,　fault　signals,　and　approximate　errors　were　bounded,　and　then　the　S-procedure　and　the　linear　matrix　inequality　(LMI)　method　were　applied　to　design　of　the　set-membership　filter.　Finally,　a　recursive　algorithm　was　developed　for　computing　the　state　estimate　ellipsoid.　The　method　for　fault　diagnosis　based　on　the　set　membership　filter　using　ellipsoid　can　not　only　estimate　fault　sizes,　but　also　can　detect　the　types　of　fault　signals.　The　simulation　results　show　that　the　method　presented　is　available　and　effective.