  This paper studies finite-horizon robust tracking control for discrete-time
linear systems, based on input-output data. We leverage behavioral theory to
represent system trajectories through a set of noiseless historical data,
instead of using an explicit system model. By assuming that recent output data
available to the controller are affected by noise terms verifying a quadratic
bound, we formulate an optimization problem with a linear cost and LMI
constraints for solving the robust tracking problem without any approximations.
Our approach hinges on a parameterization of noise trajectories compatible with
the data-dependent system representation and on a reformulation of the tracking
cost, which enables the application of the S-lemma. In addition, we propose a
method for reducing the computational complexity and demonstrate that the size
of the resulting LMIs does not scale with the number of historical data.
Finally, we show that the proposed formulation can easily incorporate actuator
disturbances as well as constraints on inputs and outputs. The performance of
the new controllers is discussed through simulations.
