Data-based control design for linear discrete-time systems with robust stability guarantees

This paper proposes a method based on virtual reference feedback tuning with robust closed-loop stability guarantees in a linear single-input and single-output setting. The proposed method is not a fully direct data-driven approach since an uncertainty set for the system is obtained through a set membership identification. Based on the uncertainty set, robust stability conditions are enforced as linear matrix inequality constraints within an optimization problem whose cost function relies on virtual reference feedback tuning. The effectiveness of the algorithm is demonstrated in a simulation example.