Many acceleration-sensitive, microgravity science experiments will require active vibration isolation from manned orbiters on which they will be mounted. The isolation problem, especially in the case of a tethered payload, is a complex three-dimensional one that is best suited to modern-control design methods. In this paper, extended H(sub 2) synthesis is used to design an active isolator (i.e., controller) for a realistic single-input-multiple-output (SIMO) microgravity vibration isolation problem. Complex mu-analysis methods are used to analyze the isolation system with respect to sensor, actuator, and umbilical uncertainties. The paper fully discusses the design process employed and the insights gained. This design case study provides a practical approach for isolation problems of greater complexity. Issues addressed include a physically intuitive state-space description of the system, disturbance and noise filters, filters for frequency weighting, and uncertainty models. The controlled system satisfies all the performance specifications and is robust with respect to model uncertainties. Hampton, R. D. and Knospe, C. R. and Allaire, P. E. and Grodsinsky, C. M. Glenn Research Center NCC3-365; RTOP 963-70-OH...