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arXiv · 2506.08034

Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control

Michael Sebek
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Abstract

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.

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Michael Sebek. 2025-06-02. Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control. https://doi.org/10.1109/med64031.2025.11073531

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