This　brief　aims　to　propose　an　effective　fault　detection　method　for　general　class　of　nonlinear　systems　in　the　context　of　the　closed-loop　system　stability.　To　this　end,　the　nonlinear　factorization　technique　is　first　used　to　model　the　faulty　nonlinear　systems,　which　can　be　represented　by　the　so-called　stable　kernel　representation　with　a　stable　parameterization　of　the　system　changes　triggered　by　faults.　Then,　the　closed-loop　system　stability　is　discussed　according　to　the　internal　stability　definition　and　the　small　gain　theorem,　respectively,　to　present　the　design　framework　of　the　fault　detection　system.　Different　from　the　traditional　fault　detection　schemes,　the　proposed　fault　detection　approach　focuses　on　detecting　whether　the　system　closed-loop　stability　is　damaged　by　faults　utilizing　the　online　measurable　system　and　controller　residual　signals.　Furthermore,　for　the　implementation　of　the　proposed　fault　detection　framework,　Takagi-Sugeno　fuzzy　models　are　applied　to　approximate　the　nonlinear　systems　and　thus　the　fault　detection　system　design　methods　can　be　provided　by　taking　advantage　of　the　linear　matrix　inequality　technique.　Finally,　a　case　study　is　used　to　verify　the　achieved　results.