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In this paper we address the problem of designing robust controllers of given structure, depending on some free design parameters. The plant to be controlled is supposed to be a linear, time invariant, continuous time system, depending on a parameter vector, known only to belong to a bounded set. Assuming that a certain number of performance specifications are given (in the frequency domain), the design is carried on by constructing an inner and an outer approximation of the set of the robustly performing design parameters. We present a method based on Bernstein polynomial expansion, which can handle the quite general case of polynomial parametric perturbations.

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