Low-dimensional observer design for stable linear systems by model reduction

TL;DR

This paper introduces a low-dimensional observer for stable LTI systems using model reduction by moment matching, achieving accurate state estimation with stability guarantees and validated through numerical simulations.

Contribution

It proposes a novel observer design based on reduced-order models that ensures asymptotic state reconstruction and input-to-state stability for stable linear systems.

Findings

Exact asymptotic state reconstruction for certain inputs.

Exponential input-to-state stability for generic inputs.

Numerical simulations demonstrate effectiveness on benchmark models.

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.