Output-Feedback Controller Synthesis for Dissipativity and $H_2$ Performance of Autoregressive Systems from Noisy Input-Output Data

In this paper we propose a data-driven output-feedback controller synthesis method for discrete-time linear time-invariant systems in a specific autoregressive form. The synthesis goal is either to achieve dissipativity with respect to a given quadratic supply rate, or to achieve given $H_2$ performance level. It is assumed that the model of the plant is unknown, except for the disturbance term. To compensate for the lack of model knowledge, we have a recorded trajectory of the controlled input and the output available for control, which can be corrupted by an unknown but bounded disturbance. Derived controller synthesis method is in the form of linear matrix inequalities and is nonconservative within the considered problem setting.