Active control of large flexible space structures is typically implemented to control only a few known elastic modes. Linear Quadratic Regulators (LQR) and Kalman-Bucy Filter (KBF) observers are usually designed to control the desired modes of vibration. Higher modes, referred to as residual modes, are generally ignored in the analysis and may be excited by the controller to cause a net destabilizing effect on the system. This is referred to as the spillover phenomenon. This dissertation considers the stabilization of the neglected dynamics of the higher modes of vibration. It aims at designing modal controllers with improved spillover stability properties. It is based on the premise that the structural dynamicist will be able to predict more vibration modes than would be practical to include in the design of the controller. The proposed method calls for designing the observer so as to improve spillover stability with minimum loss in performance. Two formulations are pursued. The first is based on optimizing the noise statistics used in the design of the Kalman-Bucy Filter. The second optimizes directly the gain matrix of the observer. The influence of the structure of the plant noise intensity matrix of the Kalman-Bucy Filter on the stability margin of the residual modes is demonstrated. An optimization procedure is presented which uses information on the residual modes to minimize spillover (i.e., maximize the stability margin) of known residual modes while preserving robustness vis-à-vis the unknown dynamics. This procedure selects either the optimum plant noise intensity matrix or the optimum observer gain matrix directly to maximize the stability margins of the residual modes and properly place the observer poles. The proposed method is demonstrated for both centralized and decentralized modal control. / Ph. D.