Observer Design over Hypercomplex Quaternions

Michael Sebek

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arXiv · 2510.15598

Observer Design over Hypercomplex Quaternions

Michael Sebek

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Abstract

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.

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Michael Sebek. 2025-10-17. Observer Design over Hypercomplex Quaternions. https://arxiv.org/abs/2510.15598

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