This thesis is concerned with the synthesis of linear-optimal heave control of electromagnetic suspension systems. The methods of computer-aided analysis and simulation were employed in this research. The intrinsic properties of electromagnetic suspension system were investigated to facilitate the synthesis and to provide guidelines for the design of electromagnets or linear motors suitable for use in suspension systems. The technique of complementary filtering, which resolves the conflicting requirements of high stiffness to load and high compliance for ride-comfort, was further developed. This led to the ability of directly comparing the merits of systems with different configurations and determining the optimal natural frequency. Together with a novel way of removing steady state gap error during the traversing of transition curves, the filtering technique was applied to the system using fixed-gain and sliding-mode variable-structure control methods. The latter method is well known for its abi1ity in maintaining closed-loop characteristics in the presence of disturbance. However, further development was required before it was applied. The resultant suspension system gave a 20% improvement in ride-quality over the best published result which was carried out under similar test conditions. Even so, theoretical analysis showed that a four-fold improvement may be possible.