The system (10; 110) is designed to control the closing of a door of a casing of a household appliance. The system (10; 110) comprises: an engagement element (11), which, in turn, comprises a support body (12), which is intended to be fitted on the casing (C); a striker (14), for being coupled, in a releasable manner, to a retaining element (16), and is mounted so as to move, relative to the support body (12), between a retracted position and an extracted position; a moving means (20) comprising a bidirectional motor (22) and a transmission mechanism (24), operated by the motor (22) and cooperates with the striker (14). The motor (22) is designed to selectively deliver to the transmission mechanism (24) a pre-opening torque, which is oriented in a direction of rotation (R1) that allows the striker (14) to be brought from the retracted position to the extracted position, and, respectively, a return torque, which is oriented in an opposite direction of rotation that allows the striker (14) to be brought from the extracted position to the retracted position.