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This paper introduces a new optimal H∞ control framework for controlling vibration of flexible structures with spatially varying disturbance. The spatially distributed nature of disturbance is taken into account in control design by introducing the concept of spatial H∞ norm for systems with spatially distributed input. A control design approach is then introduced to allow a systematic control design for controlling structural vibration caused by spatially distributed disturbance. Simulation studies on a flexible beam demonstrate that the proposed spatial control can minimise vibration for spatially varying bending moment disturbance.