Direct data-driven H2 − H∞ loop-shaping

In this paper, a direct data-driven approach is proposed to tune fixed-order controllers for unknown stable LTI plants in a mixed-sensitivity loop-shaping problem. The method requires a single set of input-output samples and it is based on simple convex optimization techniques; moreover, it guarantees internal stability as the data-length tends to infinity. Compared to a standard model-based approach, the proposed methodology theoretically guarantees the same asymptotical performance in case of correct parameterization, whereas the direct data-driven formulation is less conservative in case of undermodeling. The effectiveness of the method is illustrated via some numerical examples.