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In this paper we propose a novel methodology that allows to design, in apurely data-based fashion and for linear single-input and single-outputsystems, both robustly stable and performing control systems for trackingpiecewise constant reference signals. The approach uses both (i) VirtualReference Feedback Tuning for enforcing suitable performances and (ii) the SetMembership framework for providing a-priori robust stability guarantees.Indeed, an uncertainty set for the system parameters is obtained through SetMembership identification, where an algorithm based on the scenario approach isproposed to estimate the inflation parameter in a probabilistic way. Based onthis set, robust stability conditions are enforced as Linear Matrix Inequalityconstraints within an optimization problem whose linear cost function relies onVirtual Reference Feedback Tuning. To show the generality and effectiveness ofour approach, we apply it to two of the most widely used yet simple controlschemes, i.e., where tracking is achieved thanks to (i) a static feedforwardaction and (ii) an integrator in closed-loop. The proposed method is not fullydirect due to the Set Membership identification. However, the uncertainty setis used with the only objective of providing robust stability guarantees forthe closed-loop system and it is not directly used for the performancesoptimization, which instead is totally based on data. The effectiveness of thedeveloped method is demonstrated with reference to two simulation examples. Acomparison with other data-driven methods is also carried out.

Virtual Reference Feedback Tuning for linear discrete-time systems with robust stability guarantees based on Set Membership