Rotors suspended with electromagnetic bearings are inherently unstable; therefore feedback control is an essential part of their operation. Despite the nonlinear form of the actuator (electromagnetic bearing) dynamics, plant (rotor) model is linear time-invariant at constant rotor speed. Primary sources of uncertainty in rotor/AMB system dynamics are the varying air-gap of the electromagnetic bearings and the change in rotor dynamics with different rotational speeds due to gyroscopic effects. In order to reduce the uncertainty in the model and to enhance robust stability, adaptive Linear Parametrically-Varying (LPV) controllers scheduled via the rotor speed are designed with induced L-2-norm performance. Controllers are used for two purposes in rotor/active magnetic bearings: To stabilize the unstable open-loop dynamics and to suppress the unbalance forces that cause mechanical vibrations during the operation. Adaptive stabilization and vibration stabilization controllers designed are compared with respect to the Lyapunov functions used in the synthesis. To improve the performance of the closed-loop system with respect to possible transients during the operation, a multi-objective adaptive LPV controller is designed, trading-off robustness against performance.