A data-based image representation for continuous-time LTI systems

TL;DR

This paper introduces a numerically stable, data-driven method for representing unknown continuous-time LTI systems using derivatives approximated by algebraic differentiators, reducing computational complexity.

Contribution

It presents a novel image representation method that avoids solving differential-algebraic equations and is robust to measurement disturbances.

Findings

Effective in simulations with severe measurement disturbances

Reduces computational complexity compared to existing methods

Avoids solving differential-algebraic equations

Abstract

We derive a numerically stable method to compute an image representation of an unknown linear system only from data, leveraging a continuous-time version of Willems et al.'s fundamental lemma. To this end, we use derivatives approximated by algebraic differentiators. Our novel image representation avoids solving differential-algebraic equations and significantly reduces computational complexity by eliminating redundant degrees of freedom corresponding to the number of unknown quantities to be identified. Simulation results confirm the effectiveness of the proposed approach, even in the presence of severe measurement disturbances.