The complex mode and balanced realization methods are used separately to obtain reduced-order models for general linear asymmetric rotor systems. The methods are outlined and then applied to a typical rotor system which is represented by a 52 degree-of-freedom finite element model. The accuracy of the two methods is compared for this model and the complex mode method is found to be more accurate than the balanced realization method for the desired frequency bandwidth and for models of the same reduced order. However, with some limitations, it is also shown that the balanced realization method can be applied to the reduced-order complex mode model to obtain further order reduction without loss of model accuracy. An "Linear-Quadratic-Regulator-based leastsquares output feedback control" procedure is developed for the vibration control of rotor systems. This output feedback procedure eliminates the requirement of an observer for the use of an LQ regulator, and provides the advantage that the rotor vibration can be effectively controlled by monitoring only one single location along the rotor shaft while maintaining an acceptable performance. The procedures presented are quite general and may be applied to a large class of vibration problems including rotor-dynamics.