This thesis examines several techniques for the design of decentralized control strategies for the active control of vibrational damping in large space structures. A brief description of the finite element method is presented to explain the derivation of mathematical models of flexible structures represented by systems of linear second-order ordinary differential equations. The fundamental ideas of modal analysis are introduced to explain the concepts of vibrational modes and mode shapes, and derive the modal coordinate state space representation of flexible structures. The decentralized fixed modes of a system are defined, and several important characterizations of decentralized fixed modes are presented. Alternate characterizations of fixed modes yield additional insight into the nature: of fixed modes and often provide new methods for calculating the fixed modes of a system. The use of collocated rate feedback for robust vibrational damping control is described. It is shown that the robustness of collocated rate feedback is due to the positivity of large space structures, an extension of the mathematical concept of positive real functions to dynamic systems. Another strategy for the control of vibrational damping in large space structures, known as uniform damping control, is also described. It is shown that compared to collocated rate feedback, uniform damping control achieves increased performance at the price of decreased robustness at low frequencies. The application of decomposition techniques to the design of decentralized control laws is described, and a special type of decomposition known as an overlapping decomposition is introduced. It is shown how overlapping decompositions can be used to design control laws for systems for which the more familiar disjoint decomposition techniques often fail to yield satisfactory results. Finally, these decentralized control techniques are illustrated using a model of a proposed large space structure, the NASA CO FS mast. / Master of Science