By accelerating electrons to relativistic speeds, synchrotrons generate extremely intense and narrow beams of electromagnetic light that are used for academic research and commercial development across a range of scientific disciplines. In order to achieve optimum performance, the stability of the electron beam is a crucial parameter for synchrotrons and is achieved by a beam stabilisation system that is used to control the location of the electron beam and minimise any instability of the electron beam caused by external disturbances. Slew rate limits are common nonlinearities encountered with the actuators in synchrotron feedback systems which can impose significant limitations on the robustness and the performance of the control system, This paper describes an Internal Model Control (IMC) based anti-windup synthesis using an algebraic Riccati equation for a discrete-time control system to compensate against the performance deterioration in the presence of rate constraints. An Integral Quadratic Constraint (IQC) framework is used to analyse the robust stability of the anti-windup augmented closed loop system in the presence of norm-bounded uncertainty. The anti-windup augmented controller is implemented at Diamond Light Source, the UK's national synchrotron facility and improvements in robustness and performance were achieved with respect to the use of no anti-windup compensation. (C) 2016 Elsevier Ltd. All rights reserved.