Controller designs for the attenuation of rotor vibration are investigated. Disturbance inputs leading to vibration are classified and related to control forces and defined control states. Optimization based on the H∞ norm is then used to minimize the influence of forcing disturbances, modelling error and measurement error. The practicalities of applying the method to an experimental rotor-bearing system, with hardware constraints on controller order, are stated. The controller was implemented experimentally to conduct steady state and mass loss tests. Steady synchronous, non-synchronous and transient vibration attenuation was demonstrated. It was also shown that measurement error, caused by shaft surface roughness, can be incorporated into the controller design without the need to remove the roughness component from the measured displacement signals. If the roughness influence is not included in the design and the uncontrolled vibration is small, unnecessary control forces may result, causing an increase in vibration.