Based on mechanical - electrical - magnetic principles, the paper presents detailed analyses to build a completed mathematical model for 4 degree of freedom - rigid rotor active magnetic bearing (AMB) system. Gyroscopic effect, one of significant reasons affecting to perfonnances of system is mentioned in this research. By using the centralized approach, a state-space model for multi-input multi-output (MIMO) active magnetic bearing system is built. An optimal state feedback controller is then designed in order to directly fonnulate the perfonnance objectives of the control system and provides the best possible control system for a given set of perfonnance objectives. Zero steady-state error of system outputs is also given by the means of integrators which are added into the system. As a result, MIMO system's responses achieve quick stabilization and good perfonnances.