During　the　process　of　satellite　capture　by　a　flexible　base-link-joint　space　robot,　the　base,　joints,　and　links　vibrate　easily　and　also　rotate　in　a　disorderly　manner　owing　to　the　impact　torque.　To　address　this　problem,　a　repetitive　learning　sliding　mode　stabilization　control　is　proposed　to　stabilize　the　system.　First,　the　dynamic　models　of　the　fully　flexible　space　robot　and　the　captured　satellite　are　established,　respectively,　and　the　impact　effect　is　calculated　according　to　the　motion　and　force　transfer　relationships.　Based　on　this,　a　dynamic　model　of　the　system　after　capturing　is　established.　Subsequently,　the　system　is　decomposed　into　slow　and　fast　subsystems　using　the　singular　perturbation　theory.　To　ensure　that　the　base　attitude　and　the　joints　of　the　slow　subsystem　reach　the　desired　trajectories,　link　vibrations　are　suppressed　simultaneously,　and　a　repetitive　learning　sliding　mode　controller　based　on　the　concept　of　the　virtual　force　is　designed.　Moreover,　a　multilinear　optimal　controller　is　proposed　for　the　fast　subsystem　to　suppress　the　vibration　of　the　base　and　joints.　Two　sub-controllers　constitute　the　repetitive　learning　sliding　mode　stabilization　control　for　the　system.　This　ensures　that　the　base　attitude　and　joints　of　the　system　reach　the　desired　trajectories　in　a　limited　time　after　capturing,　obtain　better　control　quality,　and　suppress　the　multiple　flexible　vibrations　of　the　base,　links　and　joints.　Finally,　the　simulation　results　verify　the　effectiveness　of　the　designed　control　strategy.