An axial stabilizer for the rotor of a magnetic bearing provides external control of stiffness through switching in external inductances. External control also allows the stabilizer to become a part of a passive/active magnetic bearing system that requires no external source of power and no position sensor. Stabilizers for displacements transverse to the axis of rotation are provided that require only a single cylindrical Halbach array in its operation, and thus are especially suited for use in high rotation speed applications, such as flywheel energy storage systems. The elimination of the need of an inner cylindrical array solves the difficult mechanical problem of supplying support against centrifugal forces for the magnets of that array. Compensation is provided for the temperature variation of the strength of the magnetic fields of the permanent magnets in the levitating magnet arrays.