The general topic of the present book is control of turbomachinery. In particular, it deals with modeling and control techniques for variable speed centrifugal gas compression systems. The main objective of the study, presented in this book, is to design and implement multivariable controllers that regulate the centrifugal gas compressor and minimize fuel consumption of the gas turbine. In particular, the first aim is to design a multivariable controller that regulates the compressor discharge pressure as faster as possible, while preventing surge, by acting on the rotation speed, the inlet guide vanes and the anti surge valve. A further contribution, is the development of a control system that minimizes fuel consumption of the gas turbine at steady state.