An experimental and analytical study was conducted on the use of feedback stabilization to extend the stable operating range of compression and pumping systems. Prevention of surge, in aircraft gas turbine engines, an instability characterized by violent system wide oscillations in pressure, and flow, primarily motivated this research. However, such instabilities arise as a result of the non-monotonic pressure/flow relations of the axial and/or centrifugal compressors used in gas turbine engines and the results of this research can therefore be applied to many other compression and pumping systems which also employ these types of devices. The frequency response of a centrifugal compressor was measured to validate a lumped parameter model of this component. The results showed that the model is useful for control design and analysis purposes.