Synchronous vibration in rotor systems having bearings, seals, or other elements with nonlinear stiffness characteristics is prone to amplitude jump when operating close to critical speeds as there may be two or more possible whirl motions for a given unbalance condition. This paper describes research on how active control techniques may eliminate this potentially undesirable behavior. A control scheme based on feedback of rotor-stator interaction forces is considered. Model-based conditions for stability of low amplitude whirl, derived using Lyapunov’s direct method, are used to synthesize controller gains. Subsidiary requirements for existence of a static feedback control law that can achieve stabilization are also explained. An experimental validation is undertaken on a flexible rotor test rig where nonlinear rotor-stator contact interaction can occur across a small radial clearance in one transverse plane. A single radial active magnetic bearing is used to apply control forces in a separate transverse plane. The experiments confirm the conditions under which static feedback of the measured interaction force can prevent degenerate whirl responses such that a low amplitude contact-free orbit is the only possible steady-state response. The gain synthesis method leads to controllers that are physically realizable and can eliminate amplitude jump over a range of running speeds.