A theoretical linearized model is presented for the dynamics of active magnetic bearing systems in which electromagnet cores are in the shape of a cone in order to have the function of both radial and thrust bearings. In the analysis of the dynamics of electromagnets, a new model with the effects of eddy currents is considered to give a unified formulation that is applicable to a case of solid magnet cores. The linearized equations of rotor motion are much simplified when the dynamics of the electromagnets which are located in the same radial direction are equal in the two bearings. In this case, the design of a decoupling control system is considered, and the structure of the control system is obtained to give the actual control input into the electromagnet coils so that the resulting control forces may not interact in the five directions of motion.