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This paper considers the problem of designing an optimal controller for the linear static system associated with electron beam stabilisation systems in synchrotrons. The relationship between the actuators and sensors used for electron beam control in synchrotrons is modelled as a static response matrix which is typically ill-conditioned. Singular Value Decomposition (SVD) is commonly used to invert the response matrix and modes associated with small singular values are either discarded or filtered. In this paper, a robust control approach is used to determine the optimal static controller to the perturbed system. It is demonstrated how this approach compares to the use of Tikhonov regularisation for an inverse-based controller. A detailed example from the Diamond Light Source synchrotron is presented, applying both the inverse-based method and the robust control approach to stabilise electron beam motion.