From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma

In this article, we propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient our design is matrix S-lemma that will be proven in article. We provide both strict and nonstrict versions S-lemma, which are interest their own right. Thereafter, apply these results data-driven control. particular, derive nonconservative methods for quadratic stabilization, $\mathcal {H}_2$ {H}_{\infty }$ control, all terms data-based linear inequalities. contrast previous work, the dimensions decision variables independent time horizon experiment. Our approach, thus, enables control large datasets.