Observer Design over Hypercomplex Quaternions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910064215851008 |
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| author | Sebek, Michael |
| author_facet | Sebek, Michael |
| contents | We develop observer design over hypercomplex quaternions in a characteristic-polynomial-free framework. Using the standard right-module convention, we derive a right observable companion form and companion polynomial that encode error dynamics through right-eigenvalue similarity classes. We also give an Ackermann-type formula for real-coefficient target polynomials, where polynomial evaluation is similarity-equivariant. The resulting recipes place observer poles directly over quaternions and clarify when companion-coordinate updates and one-shot Ackermann formulas remain valid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Observer Design over Hypercomplex Quaternions Sebek, Michael Systems and Control 93B07, 93C05, 15A66 We develop observer design over hypercomplex quaternions in a characteristic-polynomial-free framework. Using the standard right-module convention, we derive a right observable companion form and companion polynomial that encode error dynamics through right-eigenvalue similarity classes. We also give an Ackermann-type formula for real-coefficient target polynomials, where polynomial evaluation is similarity-equivariant. The resulting recipes place observer poles directly over quaternions and clarify when companion-coordinate updates and one-shot Ackermann formulas remain valid. |
| title | Observer Design over Hypercomplex Quaternions |
| topic | Systems and Control 93B07, 93C05, 15A66 |
| url | https://arxiv.org/abs/2510.15598 |