Low-dimensional observer design for stable linear systems by model reduction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913969671766016 |
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| author | Shakib, M. F. Khalil, M. Postoyan, R. |
| author_facet | Shakib, M. F. Khalil, M. Postoyan, R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-dimensional observer design for stable linear systems by model reduction Shakib, M. F. Khalil, M. Postoyan, R. Systems and Control Optimization and Control 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. |
| title | Low-dimensional observer design for stable linear systems by model reduction |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2508.00609 |