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The design of a controller for a VSC HVDC terminal which is robust over a range of operating points is described. The operating range is first characterized as an uncertainty region around a linear nominal model using the operating points of a non-linear model. An LMI based formulation is then used to synthesize a controller which maximizes the size of the uncertainty region within which closed loop stability is maintained, while achieving closed loop pole region constraints for the nominal model. Scaling matrices are used to take advantage of the structure of the uncertainty. The controller optimization including these matrices as variables is a bilinear problem and a D-K type iterative scheme is used to find their optimizing values. The performance of the resulting controllers over the range of operating points on the non-linear model is described and compared with that of a low order controller designed using classical methods. The conservatism of the approach and the use of the pole region constraint as a tuning parameter is analyzed.