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arXiv · 2508.00609

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

M. F. Shakib·M. Khalil·R. Postoyan
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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.

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M. F. Shakib, M. Khalil, R. Postoyan. 2025-08-01. Low-dimensional observer design for stable linear systems by model reduction. https://arxiv.org/abs/2508.00609

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