A Matrix Finsler's Lemma with Applications to Data-Driven Control

Authors

Henk J. van Waarde, M. Kanat Camlibel

Year

2021

Conference Paper

Algorithm

Matrix Finsler's Lemma

Source

IEEE Conference on Decision and Control

Identifiers

arXiv 2103.13461 DOI 10.1109/CDC45484.2021.9683285

Abstract¶

In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known data-driven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.

Summary¶

Provides a matrix Finsler lemma that unifies exact-data and noisy-data direct control conditions under one quadratic-constraint view. It clarifies how several data-driven LMI synthesis results fit together and extends the machinery to Lur'e systems.