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

Henk van Waarde*, Kanat Camlibel, Mehran Mesbahi

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

77 Citations (Scopus)
162 Downloads (Pure)


In this article, we propose a new method to ob-
tain feedback controllers of an unknown dynamical system
directly from noisy input/state data. The key ingredient of
our design is a new matrix S-lemma that will be proven in
this article. We provide both strict and nonstrict versions
of this S-lemma, which are of interest in their own right.
Thereafter, we will apply these results to data-driven con-
trol. In particular, we will derive nonconservative design
methods for quadratic stabilization, H2 and H∞ control, all
in terms of data-based linear matrix inequalities. In contrast
to previous work, the dimensions of our decision variables
are independent of the time horizon of the experiment. Our
approach, thus, enables control design from large datasets.
Original languageEnglish
Pages (from-to)162-175
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - 1-Jan-2022

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