Method for controlling at least one aerodynamic stabilizer member of a hybrid helicopter, and a hybrid helicopter

A method for optimizing the operation of at least one first propeller and of at least one second propeller, which are arranged transversely on either side of an airframe of a hybrid helicopter, the hybrid helicopter including a lift rotor arranged above the airframe, the hybrid helicopter including at least one aerodynamic stabilizer member exerting a transverse lift, the aerodynamic stabilizer member being able to rotate relative to a support of the hybrid helicopter, the method comprising the following step during a control phase:

• deflection, with an autopilot system, of the aerodynamic stabilizer member into a setpoint position having, with respect to a reference position, a target deflection angle,
• wherein the target deflection angle is equal to a setpoint deflection angle at least when this setpoint deflection angle is within a range delimited by an included predetermined minimum angle and an included predetermined maximum angle, the setpoint deflection angle being calculated by the autopilot system in order to compensate for a torque exerted by the lift rotor at zero sideslip.