In order to solve the inspection problem of rotor speed and achieve the high performance control of the bearingless
induction motor, a speed-sensorless control scheme based on left-inverse system is proposed. The subsystem consisting of
rotor speed and stator currents of the torque winding is set up, and the left-invertibility of the subsystem is proved. Combining
the left-inverse system with the subsystem, the rotor speed is observed effectively. Afterwards, the speed-sensorless vector
control system of the bearingless induction motor is set up and the simulation study is carried out. Simulation results show
that the rotor speed of bearingless induction motor can be precisely estimated in a full speed operation region and the stable
speed-sensorless suspension operation can be achieved by using the proposed method.