The device according to the invention controls a polyphase inverter (10, 14, 17) intended for powering from a DC current source (CC) a polyphase rotating electric machine (1). The device is of the type of those generating commutation functions driving commutation elements (9, 13) of the inverter in such a way as to obtain a reduction of the losses in the commutation elements and a decrease of an effective current in a decoupling capacitor (16) of the source (CC). According to the invention, this reduction and this decrease are obtained by means of a set of control strategies (21, 24) determining the commutation functions by using additional degrees of freedom of the polyphase machine (1) with respect to a three-phase reference machine. The polyphase machine comprises first and second phase windings forming a first three-phase system (2, 3, 4) and a second three-phase system (5, 6, 7) with distinct neutral points (11, 15) offset angularly by a predetermined angle of offset (Θ). The first and second phase windings are linked respectively to three first and three second power arms (8, 12) formed by the commutation elements.