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This paper deals with robust control problems of mechanical systems with oscillatory bases, which are associated with robotic manipulators installed on vessels or ocean structures. For motion control of mechanical systems subject to disturbances due to the base oscillation, a linear H∞ control-based approach is developed, assuming only that the frequency range of the base oscillation is known in advance, and then it does not require any measurements of the base motion. In particular, a multiple-input/multiple-output system case is discussed, where the uncertainty parametrization of the inertia matrix plays an important role in the design technique. Some simulation results demonstrate that the designed controller desirably attenuates the disturbances and provides robust tracking performance. Additionally, an instrumental tool "extended-polytope" and its linear fractional transformation representation developed for this paper are introduced.