Low-dimensional observer design for stable linear systems by model reduction
Abstract
This paper presents a low-dimensional observer design for stable, single-input single-output, continuous-time linear time-invariant (LTI) systems. Leveraging the model reduction by moment matching technique, we approximate the system with a reduced-order model. Based on this reduced-order model, we design a low-dimensional observer that estimates the states of the original system. We show that this observer establishes exact asymptotic state reconstruction for a given class of inputs tied to the observer's dimension. Furthermore, we establish an exponential input-to-state stability property for generic inputs, ensuring a bounded estimation error. Numerical simulations confirm the effectiveness of the approach for a benchmark model reduction problem.
Cite
@article{arxiv.2508.00609,
title = {Low-dimensional observer design for stable linear systems by model reduction},
author = {M. F. Shakib and M. Khalil and R. Postoyan},
journal= {arXiv preprint arXiv:2508.00609},
year = {2025}
}