Repetitive Control (RC) has proven to be an effective and efficient way of tracking/rejecting periodic signals. Periodic signals are very common in many applications like robotics, disk drive systems, power converters and many more. However, in some applications the periodic signal to be tracked/rejected has variable period, or in other words the period of the signal is uncertain. Due to the fast growing micro-processor and micro-controller technologies most of the controllers are implemented in digital domain. This thesis contributes to the topic of performance of digital repetitive control when the frequency of the reference signal is variable. A very common real life situation of continuously variable frequency signal has arisen in electrical power system due to various factors, including increasing number of distributed generators being connected to the system. The grid connected converters are influenced by this uncontrolled frequency variations. Conventional Repetitive Control (CRC) schemes always require the frequency of the reference signal to be tracked/rejected to be a constant. CRC schemes are incapable of performing well in grid connected converter systems where the grid voltage signal acts a reference signal. The contributions of this thesis can be organized as follows: First of all, performance of the CRC scheme has been measured in terms of steady-state tracking error and Total Harmonic Distortion (THD) under time varying frequency conditions. A single phase inverter and a three-phase rectifier has been considered to evaluate the performance of the CRC techniques. The results indicate that the CRC schemes perform well only when the frequency of the reference signal is equal to the nominal frequency and sampling frequency of the digital controller is an integer multiple of the reference frequency. This thesis is dedicated to the cases where the sampling frequency of the controller is fixed. Another approach is to vary the sampling frequency in accordance to the reference frequency variations, thus obtaining an integer ratio between the two frequencies. An approach that overcomes the issue of CRC performance under time varying frequency conditions, when the sampling frequency of the digital controller is fixed, is by using a Fractional Order Repetitive Controller (FORC). The FORC uses a Lagrange interpolation based fractional delay filter which provides necessary non-integer delay to accomplish a sufficient condition required for tracking/rejecting a reference signal when the sampling frequency of the controller is no longer an integer multiple of the reference frequency. A design enhancement technique using optimal fractional delay filter has been proposed in order to analyze the stability and yields sufficient stability condition. An Advanced Repetitive Controller (ARC) is used to improve the repetitive control performance under variable or uncertain frequency reference/disturbance signal conditions. It includes a Taylor series expansion based fractional delay filter to realize necessary non-integer delay. The Taylor series expansion based fractional delay filter does not need to update sub-filter coefficients even in the presence of variable frequency reference signals. Therefore, the ARC employing a Taylor series expansion based fractional delay filter is more appropriate for applications involving frequent or continuous frequency variation. It has been shown in this thesis that in case of FORC the fractional delay filter parameters vary depending upon reference signal frequency and thus may lead to system instability if the fractional delay filter used does not operate in its optimal range. The closed-loop stability of both FORC and ARC is analyzed. Additionally, an in-depth analysis of FORC controller has been carried out to investigate the influence of every sub-system and parameters variations. The experimental validation of FORC and ARC control schemes has been performed in two different applications: a single-phase stand-alone inverter and a three-phase grid connected PWM rectifier. The PWM rectifier is used as a grid connected converter case to analyze and show the performance of the ARC controller under frequency variations. Experimental results indicate the ARC controller is capable of achieving a near zero error steady-state tracking of a variable frequency reference signal. The performance of the ARC controller and power quality of the converter is measured and presented in terms of the THD, power factor and steady-state tracking error.