Many industrial processes exhibit spatially distributed behaviour and are distributed parameter systems (DPS). Much of the current literature has focused on the control of specific types of DPS, such as those modelled by hyperbolic or parabolic partial differential equations (PDEs). Discrete state space models for these systems (termed as 2-D systems) have also been studied extensively; however, additional techniques are required to deal with boundary control problems. In this article, a discrete 2-D state space model for boundary control problems is formulated. A controller is developed for boundary control problems using the discrete state space method. Simulation results indicate that the resulting boundary controller can achieve desirable performance for setpoint tracking.