An　adaptive　H∞　fault-tolerant　vibration-suppressed　hybrid　control　algorithm　is　proposed　for　a　free-floating　flexible　space　manipulator　system　with　partial　loss　of　control　effectiveness　(PLCE)　fault.　Based　on　the　Lagrange　method　and　elastic　vibration　theory,　the　dynamic　differential　equation　of　the　system　is　deduced,　and　the　first　two　modes　reflecting　the　main　vibration　condition　of　the　flexible　link　are　intercepted　for　vibration　analysis.　According　to　the　singular　perturbation　principle,　the　system　is　decomposed　into　a　slow-varying　subsystem　describing　the　trajectory　tracking　motions　of　the　rigid　arms　and　a　fast-varying　subsystem　describing　the　modal　vibration　of　the　flexible　link.　Thus,　a　hybrid　controller　composed　of　an　adaptive　H∞　fault-tolerant　controller　of　the　slow-varying　subsystem　and　a　linear　optimal　vibration-suppressed　controller　of　the　fast-varying　subsystem　is　designed.　Compared　with　the　traditional　fault-tolerant　controllers,　the　adaptive　H∞　fault-tolerant　controller　has　the　advantage　of　not　requiring　prior　knowledge　of　actuator　fault.　The　comparison　simulation　results　show　that　the　fault-tolerant　controller　of　the　slow-varying　subsystem　has　strong　robustness　to　the　PLCE　joint　actuator　fault,　and　the　linear　optimal　vibration-suppressed　controller　of　the　fast-varying　subsystem　can　adjust　the　vibration　mode　of　the　flexible　link　to　a　lower　level,　which　verifies　the　correctness　of　the　theoretical　analysis　and　the　effectiveness　of　the　hybrid　control　strategy.　©　2020,　Editorial　Dept.　of　JA.　All　right　reserved.