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A polynomial solution to the LQG optimal control problem is presented for a system with special controller structure and robust cost-weighting terms. The controller structure has the advantages of both single- and two-degrees-of-freedom designs. The effect of introducing a common robustness weighting term in the cost index is considered. It is shown that this leads to an additional gain term in the Youla parameterised form of the controller. To illustrate the advantages of the controller structure and the influence of the robustness weighting term, a flight control system design example is presented.