We consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the gap metric. The gap perturbation margin may be more constrained for larger disturbances and for larger parametric uncertainties. Working in an L 2 setting, and within the framework of the nonlinear gap metric, universal adaptive controllers are first given achieving stabilisation for first order nominal plants, and the results are then generalised

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... relative degree one nominal plants. Necessary asymptotic properties of the robustness margins are derived for the class of controllers considered. Extensions to the L ∞ setting are also developed where two alternative designs are given. A notion of a semi-universal control design is introduced, which is the property that a bound on performance exists which is independent of the a-priori known uncertainty level, and a characterisation is given for when semi-universal designs outperform the class of memoryless controllers and the class of LTI controllers. Robust semi-universal adaptive control designs are given for nominal plants under the classical assumptions of adaptive control in both the L 2 and L ∞ settings. The results are applied throughout to explicit classes of unmodelled dynamics including the Rohrs example.