This paper deals with the problem of controlling the vibrations of large space structures by the use of a newly conceived torque actuation device, i.e., a tendon control system. It consists of a pair of tension cables transmitting a control torque to the structure at the moment arm position. The purpose of the study is twofold: first, to establish the analytical framework for low-authority control synthesis; second, to validate the proposed concept through a hardware experiment. A nonlinear optimization approach is proposed for the design of the control gains and the moment arm placement. This approach is useful when the total number of control devices is smaller than the number of critical vibrational modes, and exact pole placement is not possible. A hardware experiment has been done successfully, which shows the fundamental feasibility of the active tendon control for a highly flexible beam. However, for its practical application, further studies are needed, especially on the interactions between the dynamics of the tension cables and the flexible structure.