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The chapter 2 describes the same new dead-beat control law for three-phase surface-mounted permanent-magnet synchronous motors (brushless), based on the motor discrete-time state-space equation system, using the eigenvalues of the transition matrix. The algebraic calculation of the control voltage vector, takes account of motor parameters, of motor current measures, of torque and current set-points, and of torque, voltage, stator flux and current limits. A real-time implementation of algorithms without position sensor, is proposed with a Kalmans observer. The total uncoupling between torque and stator voltage controls is shown, as well as the torque accuracy and dynamics. The PWM and sampling periods can be chosen regardless of control law, in order to optimize inverter switching frequency and motor current shape factor.