Pseudospectra of Loewner Matrix Pencils

TL;DR

This paper explores the pseudospectra of Loewner matrix pencils to assess the robustness of system poles in data-driven modeling, providing insights into stability, transient behavior, and noise effects.

Contribution

It introduces a method to compute pseudospectra of Loewner pencils and demonstrates their use in analyzing pole stability and system behavior under various conditions.

Findings

Pseudospectra reveal pole sensitivity to data and interpolation choices

Loewner structure enables efficient pseudospectra computation

Pseudospectra analysis informs robustness of system realization

Abstract

Loewner matrix pencils play a central role in the system realization theory of Mayo and Antoulas, an important development in data-driven modeling. The eigenvalues of these pencils reveal system poles. How robust are the poles recovered via Loewner realization? With several simple examples, we show how pseudospectra of Loewner pencils can be used to investigate the influence of interpolation point location and partitioning on pole stability, the transient behavior of the realized system, and the effect of noisy measurement data. We include an algorithm to efficiently compute such pseudospectra by exploiting Loewner structure.