The objective of this paper is to develop a multivariable control system for a class of centrifugal compressors, which exploit as control signals both the rotational speed and the Inlet Guide Vane (IGV). Linear Quadratic Gaussian control with Integral action (LQGI) and Model Predictive Control (MPC) are investigated. The LQGI and MPC controllers are compared to a standard proportional integral (PI) controller, to regulate the discharge pressure of the compressor. The control algorithms are simulated and compared in different operating scenarios. Results demonstrate that the proposed multivariabe control schemes provide better performance than the single-loop PI controller, thus motivating the use of IGV for control purposes.