Bearingless machines have the potential to provide shorter rotors and achieve overall lower losses and higher energy densities than traditional technologies. However, levitation control has to overcome some further challenges. The aim of this work is to attain robust levitation in the presence of disturbances of various nature. To address dynamics dependent on varying speed, a linear parameter-varying (LPV) H _∞ -based control of magnetic suspension is applied, where speed is the scheduled parameter. The model-based centralized position control uses an inverse nonlinearity compensation and position estimation at actuator locations to decouple levitation and motoring as well as to linearize the plant model. Different control configurations and resulting performances are benchmarked from the application perspective. The tested controllers are synthesized according to the same weighting scheme. However, the control synthesis is achieved by using a Linear Matrix Inequality and a Riccati-based algorithm. A fixed-parameter H _∞ controller and an LPV controller are evaluated against a gain uncertainty. The performance of the controllers is studied based on frequency-domain analysis and time-domain simulations against accurate nonlinear plant models derived by Finite Element Modeling. Analytical results, supported by simulations with a detailed nonlinear plant model, together with selected experimental tests, assist the evaluation of the control performance of a 160 kW bearingless two-stage compressor prototype. The compressors serve as part of a 500 kW high-temperature industrial heat pump.