Increasing demands of positioning accuracy of satellites with high-precision payloads together with growing structural flexibility of their hulls, calls for active vibration isolation techniques to mitigate the impact of microvibrations on the payload. The aim of this article is to develop an linear parameter-varying (LPV) modeling and control design methodology for attenuation of frequency-varying disturbances. Application of the developed approach to a realistic space-capable multivariable vibration isolation test-bench setup shows a significant attenuation of microvibration disturbances, well-demonstrating the capabilities and deployability of the proposed method.