For　modern　complex　systems,　incipient　faults　is　usually　difficult　to　be　detected.　Under　the　assumption　that　system　process　disturbance　and　measurement　noise　are　unknown　but　bounded,　this　paper　proposes　a　novel　active　fault　detection　method　based　on　state　set-membership　estimation.　First,　a　zonotopic　Kalman　filter　is　designed　to　estimation　systems　states,　and　the　state　sets　affected　by　the　unknown　inputs　are　described　by　zonotopes.　Then,　an　auxiliary　input　signal　is　designed　such　that　the　state　sets　of　the　normal　model　are　separated　from　the　ones　of　faulty　models,　as　a　result,　incipient　faults　are　detected　successfully.　In　order　to　decrease　the　effect　of　the　auxiliary　input　to　the　practical　systems,　the　minimum　auxiliary　input　signal　is　required.　In　this　paper,　the　optimization　problem　is　transformed　into　a　mixed　integer　quadratic　programming　problem.　Compared　with　the　output　sets　based　auxiliary　input　signal　design　method,　the　proposed　technique　can　achieve　a　smaller　auxiliary　input　signal　because　of　states　set　are　not　affect　by　the　measurement　noise　at　the　next　time　instant,　and　it　has　less　conservatism.　Copyright　©　2021　Acta　Automatica　Sinica.　All　rights　reserved.