  The increase in available data and complexity of dynamical systems has
sparked the research on data-based system performance analysis and controller
design. Recent approaches can guarantee performance and robust controller
synthesis based on noisy input-state data of a single dynamical system. In this
paper, we extend a recent data-based approach for guaranteed performance
analysis to distributed analysis of interconnected linear systems. We present a
new set of sufficient LMI conditions based on noisy input-state data that
guarantees $\mathcal{H}_\infty$ performance and have a structure that lends
itself well to distributed controller synthesis from data. Sufficient LMI
conditions based on noisy data are provided for the existence of a dynamic
distributed controller that achieves $\mathcal{H}_\infty$ performance. The
presented approach enables scalable analysis and control of large-scale
interconnected systems from noisy input-state data sets.
