Data-Driven Stabilization of Continuous-Time LTI Systems from Noisy Input-Output Data

TL;DR

This paper introduces a data-driven method to design stabilizing controllers for continuous-time LTI systems directly from noisy input-output data, using LMIs and observer-based feedback.

Contribution

It develops a novel output-feedback stabilization approach that relies solely on data and noise bounds, with necessary and sufficient conditions for feasibility.

Findings

Feasibility of the LMI is necessary and sufficient for stabilization.

The method effectively handles noisy data with noise energy bounds.

Numerical simulations demonstrate the approach's effectiveness.

Abstract

We present an approach to compute stabilizing controllers for continuous-time linear time-invariant systems directly from an input-output trajectory affected by process and measurement noise. The proposed output-feedback design combines (i) an observer of a non-minimal realization of the plant and (ii) a feedback law obtained from a linear matrix inequality (LMI) that depends solely on the available data. Under a suitable interval excitation condition and knowledge of a noise energy bound, the feasibility of the LMI is shown to be necessary and sufficient for stabilizing all non-minimal realizations consistent with the data. We further provide a condition for the feasibility of the LMI related to the signal-to-noise ratio, guidelines to compute the noise energy bound, and numerical simulations that illustrate the effectiveness of the approach.