Observer Design over Hypercomplex Quaternions
This work addresses observer design for systems using hypercomplex quaternions, which is an incremental advancement in control theory.
The paper tackles the problem of observer design over hypercomplex quaternions by developing a characteristic-polynomial-free framework, resulting in recipes that directly place observer poles over quaternions and clarify conditions for valid updates and formulas.
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.