This paper deals with the study of both the stability and stabilization of an electric drive system composed of a permanent magnet machine fed by a quasi-Z-source inverter. Quasi-Z-source inverters are DC-to-AC converters that are able to step up the DC-source voltage. They can be used to adapt the DC-bus voltage to the power or the speed of the machine that they feed. This ensures the controllability of the machine over a large speed range without using field weakening strategies. This also leads to inverter losses reduction. When the DC-source voltage is large enough to control the machine, there is no need to step it up. The quasi-Z-source inverter is thus assimilated to a simple LC filter. Some stability problems can thus appear and this paper presents a way to solve them by implementing stabilization strategies aiming at having an optimal functioning of the system.