This thesis considers the problem of robust geometric regulation for tracking and disturbance rejection of systems governed by delay differential equations. It is well known that geometric regulation can be highly sensitive to system parameters and hence such designs are not always robust. In particular, when employing numerical approximations to delay systems, the resulting finite dimensional models inherit natural approximation errors that can impact robustness. This demonstrates this lack of robustness and then addresses robustness by employing versions of robust regulation that have been developed for infinite dimensional systems. Numerical examples are given to illustrate the ideas and to test the robustness of the regulator. / M.S. / Recent years have seen a surge in the everyday application of complex mechanical and electrical systems. These systems can perform complex tasks; however, the increased complexity makes it harder to control them. An example of such a system is a semi-autonomous car designed to stay within a designated lane. One of the most commonly used approaches for controlling such systems is called output regulation. In the above example, the output regulator regulates the output of the car (position of the car) to follow the reference output (the road lane). Traditionally, the design of output regulators assumes complete knowledge of the system. However, it is impossible to derive equations that govern complex systems like a car. This thesis analyzes the robustness of output regulators in the presence of errors in the system. In particular, the focus is on analyzing output regulators implemented to delay-differential equations. These are differential equations where the rate of change of states at the current time depends on the states at previous times. Furthermore, this thesis addresses this problem by employing the robust versions of the output regulators.