A fast and automatically controlled frequency-tunable radiofrequency (rf) system is installed in an rf plasma thruster consisting of a stepped-diameter insulator source tube wound by a single-turn loop antenna and a solenoid providing a magnetic nozzle, and immersed in vacuum. The frequency and the output power are controlled so as to minimize the reflection coefficient and to maintain the net power corresponding to the forward minus reflected powers at a constant level. The reproducibility of the impedance matching and the stability of the net rf power are assessed, showing the fast impedance matching within about 10 msec and the long and stable delivery of the rf power to the thruster. When increasing the rf power up to 500 W, discontinuous changes in the source plasma density, the imparted thrust, and the signal intensity of the ion beam downstream of the thruster are observed, indicating effects of the discharge mode on the thruster performance and the ion energy distribution.