Controller synthesis from noisy-input noisy-output data

We consider the problem of synthesizing a dynamic output-feedback controller for a linear system, using solely input–output data corrupted by measurement noise. To handle input–output data, an auxiliary representation of the original system is utilized. By exploiting the structure of the auxiliary system, we design a controller that robustly stabilizes all possible systems consistent with data. Notably, we also provide a novel solution to extend the results to generic multi-input multi-output systems. The findings are illustrated by numerical examples.