Polynomial Convergence of an Observer for an Infinite-Dimensional Oscillating System
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912055083139072 |
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| author | Zuyev, Alexander Kalosha, Julia |
| author_facet | Zuyev, Alexander Kalosha, Julia |
| contents | This paper is devoted to analyzing the observer convergence rate for a class of linear control systems in a Hilbert space. To characterize the polynomial stability of the observer error system, we apply the spectral theory of linear operators and explicitly construct the resolvent of the corresponding infinitesimal generator. The asymptotic behavior of the resolvent on the imaginary axis is studied to describe the rate of decay of the observation error. The estimated decay rate is illustrated through an example of an oscillating flexible structure with one-dimensional output. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial Convergence of an Observer for an Infinite-Dimensional Oscillating System Zuyev, Alexander Kalosha, Julia Optimization and Control 93B53, 93C25, 93B60, 93D99 This paper is devoted to analyzing the observer convergence rate for a class of linear control systems in a Hilbert space. To characterize the polynomial stability of the observer error system, we apply the spectral theory of linear operators and explicitly construct the resolvent of the corresponding infinitesimal generator. The asymptotic behavior of the resolvent on the imaginary axis is studied to describe the rate of decay of the observation error. The estimated decay rate is illustrated through an example of an oscillating flexible structure with one-dimensional output. |
| title | Polynomial Convergence of an Observer for an Infinite-Dimensional Oscillating System |
| topic | Optimization and Control 93B53, 93C25, 93B60, 93D99 |
| url | https://arxiv.org/abs/2410.00989 |