This dissertation presents advanced control algorithms for discrete linear repetitive processes in hard disk drives. Repetitive processes are characterized by a series of iterations or tracks, through a set of dynamics which has finite duration or length. On each iteration, a profile is produced, which in turn acts as a forcing function and contributes to the dynamics of the next iteration. As a result, it is inevitable that errors are propagated from iteration to iteration. In addition, the error propagation within each individual iteration along the time direction and the presence of repeatable error are two other common but significant problems in discrete linear repetitive processes, which aggravate the iteration-to-iteration error propagation. Such outcomes are clearly not desirable and hence appropriate control actions are needed to correct them. This dissertation first introduces the unique features and control problems in discrete linear repetitive processes. In illustration, two physical processes are studied: concentric self-servowriting process and spiral based self-servowriting process. These two repetitive processes are representative servowriting techniques used in the current hard disk drive manufacturing industry. They have the same servo system consisting of two control loops: position control loop and timing control loop, but each has its own distinct control problems and objectives. Different control algorithms have been designed in this dissertation to deal with their respective control problems and improve the control system performance. To contain the iteration-to-iteration error propagation in discrete linear repetitive processes, an iterative learning control scheme is proposed and applied in concentric self-servowriting position control loop. This is an optimization-based method which mitigates the system error by minimizing the maximum magnitude of the position deviation profile. An alternative approach, two-dimensional control scheme, is also developed for the ease of analysis. By applying the two-dimensional systems theory, the convergence problems in the iterative learning control system are translated to the stability problems in a two-dimensional system. To take a step further, this dissertation also proposes a novel adaptive feedforward control scheme to deal with the error propagation along both the time direction and the iteration direction, which is often the case for the timing control loop in concentric self-servowriting process. The control objective in this repetitive process is to attenuate the closure error within each individual track and contain the timing error propagation from track to track. To achieve this objective, the adaptive filter is designed by applying the filtered-x least mean square algorithm and the filter coefficients are adaptively updated for every servo sector by minimizing both the radial timing error energy and circumferential timing error energy. The timing control loop in spiral based self-servowriting process is a typical example of discrete linear repetitive process whose dynamics is dominated by the repeatable timing error coming from the prewritten spiral tracks. Analyzing this problem from two different perspectives, two control algorithms are derived for this repetitive process. Using the classical control theory, a recursive least square based parameter adaptation algorithm is proposed to estimate and cancel the repeatable timing error. Examined from the computer system perspective, however, this repetitive process is a real-time or event-driven control system since the write head clock is updated only at the time instants when the read head detects the sync marks from the spiral tracks, i.e. the system sampling is triggered by the read head signal. From this perspective, the repeatable timing error is interpreted as the sampling jitter in the system, which causes the sampling period to be non-uniform. To tackle with the non-uniform sampling issue in this real-time control system, a novel control scheme based on Kalman filter theory is presented. The effectiveness of the control algorithms proposed in this dissertation is verified through simulation studies using the real disk drive models and disturbance/noise data from the industry.