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arXiv · 2609.33615

A Minimum-Order Functional Observer Beyond the Darouach and Luenberger Constructions

Tyrone Fernando
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Abstract

This paper develops a general minimum-order functional observer framework that contains the classical Darouach functional observer and the reduced-order Luenberger observer as special cases. The required functional dimension is determined from the triple $(A,C,L)$ through a set of functional observability indices. The minimum dimension permitted by the algebraic observer-existence condition is characterized, and the complete family of augmentations attaining this dimension is determined. Necessary-and-sufficient spectral feasibility conditions are then established for this dimension to be the minimum achievable observer order. The resulting existence conditions reduce exactly to the Darouach conditions when no augmentation is required and to the classical observability condition in the reduced-order Luenberger case. More generally, the framework admits minimum-order functional observers of intermediate order, which may exist even when neither classical observer is available.

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Tyrone Fernando. 2026-09-27. A Minimum-Order Functional Observer Beyond the Darouach and Luenberger Constructions. https://arxiv.org/abs/2609.33615

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