Reciprocal relationship between detectability and observability in a non-uniform setting
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911320222203904 |
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| author | Huerta, Ignacio Monzón, Pablo |
| author_facet | Huerta, Ignacio Monzón, Pablo |
| contents | Building on the recent notion of non-uniform complete observability, and on the fact that this property ensures non-uniform exponential detectability, this paper establishes the converse implication under suitable additional assumptions. Specifically, we investigate conditions under which non-uniform exponential detectability guarantees non-uniform complete observability. Our approach is based on a refined analysis of the associated output feedback systems and on the preservation of non-uniform observability properties under such feedback transformations. These results extend the classical equivalence between observability and detectability beyond the uniform framework and provide new tools for the qualitative analysis of time-varying control systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reciprocal relationship between detectability and observability in a non-uniform setting Huerta, Ignacio Monzón, Pablo Optimization and Control Classical Analysis and ODEs Building on the recent notion of non-uniform complete observability, and on the fact that this property ensures non-uniform exponential detectability, this paper establishes the converse implication under suitable additional assumptions. Specifically, we investigate conditions under which non-uniform exponential detectability guarantees non-uniform complete observability. Our approach is based on a refined analysis of the associated output feedback systems and on the preservation of non-uniform observability properties under such feedback transformations. These results extend the classical equivalence between observability and detectability beyond the uniform framework and provide new tools for the qualitative analysis of time-varying control systems. |
| title | Reciprocal relationship between detectability and observability in a non-uniform setting |
| topic | Optimization and Control Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2512.13589 |