This thesis presents a dynamic analysis and a control system for a flexible space manipulator, the Deployable Robotic Manipulator or DRM, which has a deployable/retractable link. The link extends (or retracts) from the containing slewing link of the manipulator to change the DRM's length and hence its workspace. This makes the system dynamics time varying and therefore any control strategy has to adapt to this fact. The aim of the control system developed is to slew the manipulator through a predetermined angle given a maximum angular acceleration, to reduce flexural vibrations of the manipulator and to have a certain degree of robustness, all of this while carrying a payload and while the length of the manipulator is changing. The control system consists of a slewing motor that rotates the manipulator using the open-loop assumed torque method and two reaction wheel actuators, one at the base and one at the tip of the manipulator, which are driven by a closed-loop damping control law. Two closed-loop control laws are developed, a linear control law and a Lyapunov based control law. The linear control law is based on collocated output feedback. The Lyapunov control law is developed for each of the actuators using Lyapunov stability theory to produce vibration control that can achieve the objectives stated above for different payloads, while the manipulator is rotating and deploying or retracting. The response of the system is investigated by computer simulation for two-dimensional vibrations of the deployable manipulator. Both the linear and Lyapunov based feedback control laws are found to eliminate vibrations for a range of payloads, and to increase the robustness of the slewing mechanism to deal with uncertain payload characteristics.