  This paper studies worst-case robust optimal tracking using noisy
input-output data. We utilize behavioral system theory to represent system
trajectories, while avoiding explicit system identification. We assume that the
recent output data used in the data-dependent representation are noisy and we
provide a non-conservative design procedure for robust control based on
optimization with a linear cost and LMI constraints. Our methods rely on the
parameterization of noise sequences compatible with the data-dependent system
representation and on a suitable reformulation of the performance
specification, which further enable the application of the S-lemma to derive an
LMI optimization problem. The performance of the new controller is discussed
through simulations.
