Controller synthesis for input-state data with measurement errors

We consider the problem of designing a state-feedback controller for a linear system, based only on noisy input-state data. We focus on input-state data corrupted by additive measurement errors, which, albeit less investigated, are as relevant as process disturbances in applications. For energy and instantaneous bounds on these measurement errors, we derive linear matrix inequalities for controller design where the one for the energy bound is actually equivalent to robust stabilization of all systems consistent with the noisy data points.