High-precision　measurements　of　base　attitude　and　link　joint　displacements　and　flexible　link　coordinate　are　available　on　flexible　space　robot　manipulators.　In　contrast,　base　angular　velocity　and　link　joint　velocity　and　flexible　link　coordinate　rate　measurements　which　increase　the　cost　are,　in　many　cases,　contaminated　by　noise.　It　is　therefore　economically　and　technically　interesting　to　investigate　the　possibility　of　controlling　flexible　space　robot　dynamics　by　only　using　angular　position　measurements　and　flexible　deformation.　Firstly　the　dynamic　model　of　a　free-flying　space　manipulator　with　a　flexible　link　is　established　by　applying　the　Lagrange　equations.　Secondly　singular　perturbation　model　of　the　space　flexible　manipulator　system　is　obtained　by　using　two-time　scale　control　theory,　in　which　the　system　is　decoupled　into　slow　(rigid)　and　fast　(flexible)　subsystems.　Then　a　composite　controller　which　consists　of　a　slow　control　component　and　a　fast　control　component　is　proposed.　The　fast　controller　is　designed　with　the　estimated　velocity　by　linear　observer　to　damp　out　the　vibration　of　the　flexible　link　using　optimal　Linear　Quadratic　Regulator　(LQR)　method.　A　sliding　observer　based　robust　control　algorithm　is　applied　to　control　the　slow　subsystem　with　unknown　payload　parameters　and　bounded　disturbances　to　track　the　desired　trajectory.　Finally　the　numerical　simulation　is　carried　out,　which　confirms　the　controller　proposed　is　feasible　and　effective.　Copyright　©　2013　by　the　International　Astronautical　Federation.