In this paper, the partitioned rotor flux switching permanent magnet machine with ferrite permanent magnet is proposed. By the adoption of the partitioned rotor configuration, the stator flux leakage is eliminated and the permanent magnet utilization is improved. The ferrite permanent magnet machine often suffers from irreversible demagnetization due to the inherent relatively low coercivity of ferrite permanent magnet. To mitigate the machine irreversible demagnetization risk, an improved partitioned rotor flux switching permanent magnet machine with hybrid permanent magnet topology is also proposed. Two little pieces of rare-earth permanent magnet are installed at the corners of ferrite permanent magnet, thus forming the hybrid permanent magnet topology. And the demagnetization mechanisms of both machines are clarified by the magnetic equivalent circuit method, which prove that the rare-earth permanent magnet offer magnetic protection function for the ferrite permanent magnet. Furthermore, by the 2-D finite element analysis, the demagnetization characteristics and the electromagnetic performances of the two machines are quantitively assessed, revealing that the demagnetization risk is reduced significantly. Both theoretical analysis and simulation results verify that the improved machine can not only maintain low-cost design, but also possess enhanced demagnetization withstand capability and competitive electromagnetic performances as expected.