From Reference Model Selection to Controller Validation: Application to Loewner Data-Driven Control

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 letter, we propose a method to build such a reference model, both reproducible by the system and having a desired behavior. 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 Loewner data driven control (L-DDC) 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.