Observability of linear systems on the Heisenberg Lie group
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912293387763712 |
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| author | Cavalheiro, Thiago Matheus Santana, Alexandre José Ayala, Victor |
| author_facet | Cavalheiro, Thiago Matheus Santana, Alexandre José Ayala, Victor |
| contents | In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time, even when direct measurements are impossible. By harnessing observability, we can accurately estimate the complete state of a system and reconstruct its dynamics using just limited information. In this work, we will find conditions for observability of linear systems in the three dimensional Heisenberg group $\mathcal{H}$. Considering the homomorphisms between the group and its simply connected subgroups, whose kernel is denoted by $K$, we will find sufficient conditions for observability on the system using a quotient space $\mathcal{H}/K$ as the output. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Observability of linear systems on the Heisenberg Lie group Cavalheiro, Thiago Matheus Santana, Alexandre José Ayala, Victor Optimization and Control In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time, even when direct measurements are impossible. By harnessing observability, we can accurately estimate the complete state of a system and reconstruct its dynamics using just limited information. In this work, we will find conditions for observability of linear systems in the three dimensional Heisenberg group $\mathcal{H}$. Considering the homomorphisms between the group and its simply connected subgroups, whose kernel is denoted by $K$, we will find sufficient conditions for observability on the system using a quotient space $\mathcal{H}/K$ as the output. |
| title | Observability of linear systems on the Heisenberg Lie group |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.19890 |