The　trajectory　tracking　and　vibration　suppression　control　for　free-floating　flexible　space　manipulator　with　disturbance　were　discussed.　With　the　momentum　conservation　relations,　system　dynamics　model　was　set　up　by　the　Lagrange　method.　Using　the　two-time　scale　decomposition　of　singular　perturbation　method,　and　the　system　was　decomposed　into　a　slow　subsystem　which　was　described　joint　trajectory　tracking　and　a　fast　subsystem　which　was　described　the　vibration　of　flexible　manipulator.　Then　a　composite　controller　consisting　of　a　slow　control　component　and　a　fast　control　component　was　proposed.　For　the　slow　subsystem,　adaptive　fuzzy　H∞　control　algorithm　was　designed,　the　fuzzy　logic　system　was　used　to　approximate　the　system　uncertainty,　and　a　robust　H∞　control　was　used　to　overcome　the　fuzzy　approximation　errors　and　eliminate　the　influences　of　the　external　disturbance　on　the　output　tracking　errors.　For　the　fast　subsystem,　optimal　linear　quadratic　regulator(LQR)　was　designed　to　damp　out　the　vibration　of　the　flexible　links.　Based　on　Lyapunov　stability　theory,　it　is　proved　that　this　algorithm　can　ensure　the　control　system　is　asymptotically　stable.　Numerical　simulation　results　illustrate　that　the　proposed　controller　is　reliable　and　effective,　this　control　scheme　makes　the　tracking　errors　of　the　system　and　the　flexible　vibrations　quickly　convergence.　©　2016,　China　Mechanical　Engineering　Magazine　Office.　All　right　reserved.