A new method is presented for vibration control of distributed gyroscopic systems. The control is formulated in the Laplace transform domain. The transfer function a closed-loop system, consisting of the plant, a feedback control law and the dynamics of the sensing and actuation devices, is derived. Stability analyses of the closed-loop system use both the root locus method and the generalized Nyquist criterion. Two stability criteria are obtained. Design of stabilizing controllers is carried out for both colocation and noncolocation of the sensor and actuator. The effects of time-delay and noncolocation of the sensor and actuator on the system stability are analyzed. In addition, the relationship between the root locus method and the generalized Nyquist criterion is discussed.