This　paper　studies　the　problem　of　fault　estimations　for　linear　continuous-time　systems　with　polytopic　uncertainties.　A　fault　detection　filter　is　designed,　which　minimizes　the　disturbance　effects　on　residual　output　and　maximizes　the　fault　effects　on　residual　output.　By　using　the　Generalized　Kalman-Yakubovich-Popov　(GKYP)　Lemma,　the　design　problem　is　formulated　to　solving　a　set　of　linear　matrix　inequalities　(LMIs).　A　numerical　example　is　given　to　illustrate　the　effectiveness　of　the　method　proposed　in　this　paper.