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The well-known and commonly accepted finite dimensional model qualitatively describing surge instabilities in centrifugal (and axial) compressors is considered. The problem of global output feedback stabilization for it is solved. The solution relies on two new criteria for global stability proposed for a class of nonlinear systems exploiting quadratic constraints for infinite sector nonlinearities. The constructive steps in developing a family of output feedback controllers based on these stability tests are presented. Performance of the closed-loop systems are illustrated by simulations.