发表机构
University of Western Australia（西澳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个统一的最小阶函数观测器框架，涵盖Darouach与Luenberger观测器为特例，通过功能可观测性指数确定最小维数，并给出谱可行性条件，支持中间阶数观测器。
AI 中文摘要
本文开发了一个一般的最小阶函数观测器框架，该框架将经典的Darouach函数观测器和降阶Luenberger观测器作为特例包含在内。所需的功能维数由三元组$(A,C,L)$通过一组功能可观测性指数确定。代数观测器存在条件所允许的最小维数被刻画，并且达到该维数的完整增广族被确定。随后，针对该维数成为可实现的最小观测器阶数，建立了必要且充分的谱可行性条件。当不需要增广时，所得存在条件精确地退化为Darouach条件；在降阶Luenberger情形下，则退化为经典可观测性条件。更一般地，该框架允许中间阶数的最小阶函数观测器，这些观测器即使在经典观测器均不可用时也可能存在。
英文摘要
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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