Data-driven stabilization of continuous-time systems with noisy input-output data

TL;DR

This paper develops a data-driven method for stabilizing continuous-time systems using noisy input-output data, providing conditions and controllers based on linear matrix inequalities, and compares data informativity in noisy and noise-free cases.

Contribution

It introduces an operator-based characterization of system consistency with noisy data and derives a necessary and sufficient condition for stabilization using behavioral theory.

Findings

Linear matrix inequalities for stabilization controllers

Characterization of data informativity in noisy and noise-free cases

Operator-based system consistency analysis

Abstract

We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next, combining this characterization with behavioral theory, we derive a necessary and sufficient condition for the noisy data to be informative for quadratic stabilization. This condition is formulated as linear matrix inequalities, whose solution yields a stabilizing controller. Finally, we characterize data informativity for system identification in the noise-free setting.