After　the　flexible　space　robot　captures　the　target　satellite,　the　dynamic　model　of　the　composite　system　consists　of　the　motion　coupling　between　the　manipulator　and　the　base,　and　the　rigid　flexible　coupling　between　the　flexible　base,　flexible　joint,　flexible　link　elastic　deformation　and　the　rigid　motion　of　the　combined　system.　It＇s　a　complex　multibody　system.　The　impact　analyses　of　the　flexible　space　robot　capturing　a　target　and　stability　control　problem　in　the　post-impact　process　were　discussed　in　the　paper.　a　linear　feedback　control　algorithm　is　designed　to　realize　the　stabilization　control　of　the　base　attitude　and　the　manipulator　joint　angle　of　the　combination　system.　In　order　to　suppress　the　flexible　vibrations　of　the　links　of　the　slow　subsystem,　a　hybrid　trajectory　reflecting　the　flexible　vibration　of　the　links　and　the　rigid　motion　of　the　system　is　constructed　by　using　virtual　force　conception,　and　compound　controller　on　virtual　force　conception　is　proposed　to　ensure　the　accurate　tracking　of　the　trajectory　of　the　base　and　joints,　while　actively　suppressing　the　flexible　vibrations　of　the　links.　For　the　fast　subsystem,　the　linear　quadratic　optimal　control　algorithm　is　used　to　suppress　the　flexible　vibration　of　the　base　and　joints.　Finally,　the　effectiveness　of　the　proposed　control　algorithm　is　verified　by　numerical　simulations.　Copyright　©　2021　by　the　International　Astronautical　Federation　(IAF).　All　rights　reserved.