The article proposes a nonlinear optimal control method for a gas centrifugal compressor actuated by a five-phase induction motor. To achieve high-torque and power in gas compressors, five-phase induction motors appear to be advantageous comparing to three-phase synchronous or asynchronous electric machines. The dynamic model of the integrated compression system which comprises the gas compressor and the five-phase induction motor, is first written in a nonlinear and multivariable state-space form. It is proven that the electrically-driven gas-compression system is differentially flat. Next, this system is linearized around a temporary operating point that is recomputed at each sampling interval. The linearization is based on first-order Taylor series expansion and the computation of the Jacobian matrices of the state-space model of the integrated system. For the linearized state-space description of the compressor and five-phase IM a stabilizing optimal (H-infinity) feedback controller is designed. This controller achieves a solution to the nonlinear optimal control problem of the compressor and five-phase IM system under model uncertainty and external perturbations. The feedback gains of the controller are computed by solving an algebraic Riccati equation at each iteration of the control method. Lyapunov analysis is used to demonstrate global stability for the control loop.