Loewner-based Data-driven Iterative Structured Control Design

Stability enforcement remains a challenge in data-driven control paradigms, where no parametrised model of the system is available. For instance, the system's instabilities can be estimated in order to enforce a closed-loop stability constraint on the controller reduction step. In order to avoid this preliminary estimation of instabilities, this paper proposes to embed a closed-loop stability constraint in the design. To that extent, an optimization problem is formulated in order to improve matching between the reference model and the closed-loop while maintaining internal stability. The proposed iterative procedure to solve this problem is illustrated on two numerical examples.