Additive manufacturing (AM) is a set of manufacturing processes that have promise in the production of complex, functional structures that cannot be fabricated with conventional manufacturing, and in the repair of high-value parts. However, a significant challenge to the adoption of AM processes to these applications is proper process control. Because AM processes exhibit dynamics in two dimensions--within a layer and from one layer to the next--unconventional tools are needed to enable the necessary process control. Here, stability analysis and control design are presented for the laser metal deposition (LMD) process, based on a previously developed 2-D modeling framework. Linear repetitive process results are extended in order to analyze the stability of this class of systems. A layer-to-layer process controller is developed using a spatial dynamic model of the process and layer-domain closed-loop poles. The stability analysis and control methodology are applied to the LMD process, which is known to exhibit layer-to-layer instability in both open-loop and in-process control depositions. Walls are experimentally fabricated using constant process parameters and the proposed control methodology. The results demonstrate that the proposed control methodology is able to track the reference height and remove the unstable ripple dynamic that naturally occurred in the open-loop deposition.