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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.08034 |
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| _version_ | 1866912602118946816 |
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| author | Sebek, Michael |
| author_facet | Sebek, Michael |
| contents | We present new polynomial-based methods for discrete-time quaternionic systems, highlighting how noncommutative multiplication modifies classical control approaches. Defining quaternionic polynomials via a backward-shift operator, we examine left and right fraction representations of transfer functions, showing that right zeros correspond to similarity classes of quaternionic matrix right eigenvalues. We then propose a feedback design procedure that generalizes pole placement to quaternions - a first approach using a genuine quaternionic polynomial equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control Sebek, Michael Systems and Control We present new polynomial-based methods for discrete-time quaternionic systems, highlighting how noncommutative multiplication modifies classical control approaches. Defining quaternionic polynomials via a backward-shift operator, we examine left and right fraction representations of transfer functions, showing that right zeros correspond to similarity classes of quaternionic matrix right eigenvalues. We then propose a feedback design procedure that generalizes pole placement to quaternions - a first approach using a genuine quaternionic polynomial equation. |
| title | Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2506.08034 |