Data-Driven Stabilization for Input-Output AR Systems With Measurement Noise-Corrupted Data^*

This article studies dynamic output-feedback stabilization for linear time-invariant input-output autoregressive systems, directly from measured data. The input-output data are assumed to be corrupted by measurement noise, with both energy and instantaneous bounds considered. For each case, a data-driven parametrization of all systems compatible with the data is derived via a matrix elimination result. Leveraging Petersen’s lemma and a lossy matrix S-procedure, we formulate linear matrix inequalities to synthesize controllers that stabilize all compatible systems. The effectiveness of the proposed methods is demonstrated through numerical examples.