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Considering discrete-time linear time-varying systems with unknown dynamics, controllers guaranteeing bounded closed-loop trajectories, optimal performance and robustness to process and measurement noise are designed via convex feasibility and optimisation problems involving purely data-dependent linear matrix inequalities. For the special case of periodically time-varying systems, infinite-horizon guarantees are achieved based on finite-length data sequences.
Nortmann et al. (Tue,) studied this question.