The current changes in the grid driven by the energy transition demands better performance from the devices connected to it. This involves the continuous supply of energy despite the presence of distortion and events of high voltage and frequency volatility. In this direction, the present work contributes by introducing a proportional-resonant controller for power inverters with the capability of tracking distorted references of varying frequency. Since the controller is able of adapting the frequency of the resonant terms, we refer to it as adaptive proportional-resonant controller. In this work, not only the aforementioned controller is presented, but a formal proof of its capability of tracking references of varying frequency is given. Furthermore, it is shown that the proposed controller also guarantees the stability of the inverter when connected to a non-ideal grid. These properties are also illustrated via numerical simulation.