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In this paper a new approach is proposed to design locally optimal robust output-feedback controllers. It is iterative by nature, and starting from any initial feasible controller it performs local optimization over a suitably defined non-convex function at each iteration. The approach features the properties of computational efficiency, guaranteed convergence to a local optimum, and applicability to a very wide range of problems. The paper also proposes a fast procedure for initially feasible controller computation based on LMIs. The design objectives considered are H2, H∞, and pole-placement constraints. The procedure consists of two steps: first an optimal robust mixed H2/H∞/pole-placement state-feedback gain is designed, which is consequently kept fixed at the second step during the design of the remaining controller matrices. The approach is demonstrated on a model of one joint of a real-life space robotic manipulator.