The purpose of the Phase 1 effort was to investigate and demonstrate the feasibility of a new class of computational algorithms for the design of high performance control laws for flexible space structures based on frequency response modeling and to consider advanced techniques for the implementation of real time control for precision (wide bandwidth) applications. Typical applications requiring advanced realtime control of flexible space structure include vibration suppression and isolation of payload subsystems. Performance of vibration suppression and isolation systems are critical factors effecting achievable levels of performance for space based optical systems. In the Phase 1 effort, a prototype software code was developed for testing computational algorithms for spectral factorization, causal projection, and coprime factorization-critical steps in frequency domain design of precision control laws. Keywords: Computer programs; Mathematical models; Algorithms.