The compressor recycle system is the main focus of this thesis. When the mass flow through a compressor becomes too low, the compressor can plunge into surge. Surge is a term that is used for axisymmetric oscillation through a compressor and is highly unwanted. The recycle system feeds compressed gas back to the intake when the mass flow becomes too low, and thereby act as a safety system.A mathematical model of the recycle system is extended and simulated in SIMULINK. The mathematical model contains the compressor characteristic, which is a function that defines the axisymmetric behavior through a compressor at different flows. The compressor characteristic is often modeled as a third order equation, but here it is modeled as a bivariate cubic spline approximation of measurement points. It is shown how a typical industry-setup of the recycle system works to avoid surge.The recycle system is proven to be stable independent of recycle flow, as long as the slope of the compressor characteristic is negative. Three control laws have been derived by the use of block backstepping. The simplest one of them guarantees semiglobal exponential stability.