An engine system includes a compressor system which is at least partially driven by an electric motor, and a turbine system. The system includes a detector for detecting an actual supercharging pressure. A target supercharging pressure is determined based on operational conditions of the engine. A first control demand value is calculated to drive the motor controller, such that the actual supercharging pressure approaches the target supercharging pressure. A target value of the first control demand value is determined based on the operational conditions of the engine. A second control demand value, a difference between the target value and the first control command value is applied to the turbine system to adjust the rotation of the turbine such that the first control demand value converges to the target value.