Data-driven control via Petersen’s lemma

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an open-loop experiment. In presence noise data, we have that set dynamics could generated data need designed controller to stabilize such data-consistent robustly. For this data-driven with noisy advocate use popular tool robust control, Petersen's lemma. cases by linear polynomial systems, conveniently express uncertainty captured through matrix ellipsoid, show specific form ellipsoid makes it possible apply lemma all mentioned cases. way, obtain necessary sufficient conditions for stabilization systems inequality. The representation enables insights interpretations laws. same also (convex) sum-of-squares programs. findings are illustrated numerically.