The choice of a reference model in data-driven control techniques is a critical step. Indeed, it should represent the desired closed-loop performances and be achievable by the plant at the same time. In this paper, we propose a method to build such a reference model, both reproducible by the system and having a desired behaviour. It is applicable to Linear Time-Invariant (LTI) monovariable systems and relies on the estimation of the plant's instabilities through a data-driven stability analysis technique. The L-DDC (Loewner Data Driven Control) algorithm is used to illustrate the impact of the choice of the reference model on the control design process. Finally, the proposed choice of specifications allows to use a controller validation technique based on the small-gain theorem.

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The L-DDC (Loewner Data Driven Control) algorithm is a data-driven controller design method based on frequency-domain input-output data. The identification of the plant is skipped and the controller is designed directly from the measurements using the Loewner approach, known for model approximation and reduction. However, in the L-DDC method, the identified controller is not guaranteed to be stable and the effect of noise on the identified controller is unknown. In this article, we ensure the stability of the controller and propose a solution to deal with noisy data. The method is validated on a numerical example.

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