The switching frequency of the power electronic devices used in large synchronous motor drives is usually kept low (less than 1 kHz) to reduce the switching losses and to improve the converter power capability. However, this results in a couple of problems, e.g. an increase in the harmonic components of the stator current, and an undesired cross-coupling between the magnetization current component ($i_m$) and the torque component ($i_t$). In this paper, a novel complex matrix model of electrically excited synchronous motors (EESM) was established with a new control scheme for coping with the low switching frequency issues. First, a hybrid observer was proposed to identify the instantaneous fundamental component of the stator current, which results in an obvious reduction of both the total harmonic distortion (THD) and the low order harmonics. Then, a novel complex current controller was designed to realize the decoupling between $i_m$ and $i_t$. Simulation and experimental results verify the effectiveness of this novel control system for EESM drives.