Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control
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.
Cite
@article{arxiv.2506.08034,
title = {Exploring Noncommutative Polynomial Equation Methods for Discrete-Time Quaternionic Control},
author = {Michael Sebek},
journal= {arXiv preprint arXiv:2506.08034},
year = {2025}
}
Comments
Published in: 2025 33rd Mediterranean Conference on Control and Automation (MED), Tangier, Morocco, 2025. DOI: 10.1109/MED64031.2025.11073531. \c{opyright} 2025 IEEE. Personal use permitted; all other uses by permission of IEEE. Published version: https://doi.org/10.1109/MED64031.2025.11073531