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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.21425 |
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| _version_ | 1866910053363089408 |
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| author | Sebek, Michael |
| author_facet | Sebek, Michael |
| contents | We present an extension of state-feedback pole placement for quaternionic systems, based on companion forms and the Ackermann formula. For controllable single-input quaternionic LTI models, we define a companion polynomial that annihilates its companion matrix, characterize spectra via right-eigenvalue similarity classes, and prove coefficient-matching design in controllable coordinates. We then derive a coordinate-free Ackermann gain expression valid for real target polynomials, and state its scope and limitations. Short examples demonstrate correctness, practical use, and numerical simplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternionic Pole Placement via Companion Forms and the Ackermann Formula Sebek, Michael Systems and Control 93B55, 93C05, 15A66, 15A21 We present an extension of state-feedback pole placement for quaternionic systems, based on companion forms and the Ackermann formula. For controllable single-input quaternionic LTI models, we define a companion polynomial that annihilates its companion matrix, characterize spectra via right-eigenvalue similarity classes, and prove coefficient-matching design in controllable coordinates. We then derive a coordinate-free Ackermann gain expression valid for real target polynomials, and state its scope and limitations. Short examples demonstrate correctness, practical use, and numerical simplicity. |
| title | Quaternionic Pole Placement via Companion Forms and the Ackermann Formula |
| topic | Systems and Control 93B55, 93C05, 15A66, 15A21 |
| url | https://arxiv.org/abs/2509.21425 |