A system and method are provided for controlling the temperature of engine bleed air from a turbofan gas turbine engine. The system includes a fan air valve and a fan air valve controller. The fan air valve is adapted to receive a flow of fan air from a turbofan gas turbine engine intake fan. The fan air valve is coupled to receive valve position commands and is configured, in response to the valve position commands, to move to a valve position to thereby control the engine bleed air temperature. The fan air valve controller is configured to implement a linear quadratic regulator (LQR) control. The fan air valve controller is adapted to receive a plurality of sensor signals, each sensor signal representative of one or more system parameters, and is configured, in response to the sensor signals, to supply the valve position commands to the fan air valve.