The paper presents the sensitivity and stability margin analyses of the flexible rotor supported by active magnetic bearings (AMBs) with the robust optimal vibrations control. The modal representation of the rotor finite element model (FEM) is investigated. Then, the open-loop system of the AMBs flexible rotor is established and critical speed analysis due to variation of bearing stiffness is performed. For the open-loop setup, the non-collocation effect of displacement sensors and magnetic actuators due to control stability problem is considered. The frequency mode analysis of the collocation and non-collocation system is presented. Next, the -synthesis control of 4-DOF AMBs rotor is investigated. The design process of -controllers, which cover uncertainty design and performance shape by chosen weighting function is shortly described. Then, the sensitivity function is calculated and used to evaluate the AMBs rotor stability margin for the -control and the PID control. The performance of the -controller are verified in experimental tests.