Under　the　conditions　of　joint　torque　output　dead-zone　and　external　disturbance,　the　trajectory　tracking　and　vibration　suppression　for　a　free-floating　space　robot　(FFSR)　system　with　elastic　base　and　flexible　links　were　discussed.　First,　using　the　Lagrange　equation　of　the　second　kind,　the　dynamic　model　of　the　system　was　derived.　Second,　utilizing　singular　perturbation　theory,　a　slow　subsystem　describing　the　rigid　motion　and　a　fast　subsystem　corresponding　to　flexible　vibration　were　obtained.　For　the　slow　subsystem,　when　the　width　of　dead-zone　is　uncertain,　a　dead-zone　pre-compensator　was　designed　to　eliminate　the　impact　of　joint　torque　output　dead-zone,　and　an　integral　sliding　mode　neural　network　control　was　proposed.　The　integral　sliding　mode　term　can　reduce　the　steady　state　error.　For　the　fast　subsystem,　an　optimal　linear　quadratic　regulator(LQR)　controller　was　adopted　to　damp　out　the　vibration　of　the　flexible　links　and　elastic　base　simultaneously.　Finally,　computer　simulations　show　the　effectiveness　of　the　compound　control　method.　©　2020　Editorial　Department　of　Journal　of　Beijing　Institute　of　Technology.