This thesis presents the multivariable controller design and implementation for a high-precision 6-degree-of-freedom (6-DOF) magnetically levitated (maglev) positioner. The positioner is a triangular single-moving part that carries three 3-phase permanent-magnet linear-levitation-motor armatures. The three planar levitation motors not only generate the vertical force to levitate the triangular platen but control the platen's position in the horizontal plane. All 6-DOF motions are controlled by magnetic forces only. The positioner moves over a Halbach magnet matrix using three sets of two-axis Hall-effect sensors to measure the planar motion and three Nanogage laser distance sensors for the vertical motion. However, the Hall-effect sensors and the Nanogage laser distance sensors can only provide measurements of the displacement of all 6-axis. Since we do not have full-state feedback, I designed two Linear Quadratic Gaussian (LQG) multivariable controllers using a recursive discrete-time observer. A discrete hybrid H2/H(infinity) filter is implemented to obtain optimal estimates of position and orientation, as well as additional estimates of velocity and angular velocity for all 6 axes. In addition, an analysis was done on the signals measured by the Hall-effect sensors, and from there several digital filters were tested to optimize the readings of the sensors and obtain the best estimates possible. One of the multivariable controllers was designed to close the control loop for the three-planar-DOF motion, and the other to close the loop for the vertical motion, all at a sampling frequency of 800 Hz. Experimental results show a position resolution of 1.5 micrometers with position noise of 0.545 micrometers rms in the x-and y-directions and a resolution of less than 110 nm with position noise of 49.3 nm rms in z.