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
本文从代数条件最小阶到功能可观测性上界，逐阶刻画线性功能观测器，给出最小谱可行阶数，并统一Darouach与Luenberger阶数为特例。
AI 中文摘要
本文给出了线性功能观测器在代数观测器条件所允许的最小维数与由功能可观测性确定的上端点之间的逐阶刻画。功能可观测性指标确定了最小代数容许阶数 $$ q_0=\sum_{j=1}^r\eta_j, $$ 其中 $r$ 是要估计的独立功能数，$\eta_j$ 是与第 $j$ 个功能相关的功能可观测性指标。对于具有 $p$ 个独立测量输出的 $n$ 维系统，令 $n_0$ 表示可观测性矩阵的秩。在功能可观测性下，功能观测器阶数范围的上端点为 $n_0-p$。在这两个端点之间的每个指定阶数上，对代数条件和谱观测器条件进行了刻画。原始状态空间中的零空间表示分别给出了代数条件和谱条件的秩和矩阵束刻画。最小观测器阶数作为所得阶数谱中最小的谱可行阶数获得。两个端点包括经典的Darouach和Luenberger阶数作为特殊情况：当 $q_0=r$ 时，下端点退化为Darouach阶数；而在完全可观测性下，上端点退化为Luenberger阶数 $n-p$。
英文摘要
This paper gives an order-by-order characterization of linear functional observers between the minimum dimension permitted by the algebraic observer condition and the upper endpoint determined by functional observability. Functional observability indices determine the minimum algebraically admissible order $$ q_0=\sum_{j=1}^rη_j, $$ where $r$ is the number of independent functionals to be estimated and $η_j$ is the functional observability index associated with the $j$th functional. For an $n$-dimensional system with $p$ independent measured outputs, let $n_0$ denote the rank of the observability matrix. Under functional observability, the upper endpoint of the functional-observer order range is $n_0-p$. The algebraic and spectral observer conditions are characterized at each prescribed order between these two endpoints. A nullspace representation in the original state space yields rank and matrix-pencil characterizations of the algebraic and spectral conditions, respectively. The minimum observer order is obtained as the smallest spectrally feasible order in the resulting order spectrum. The two endpoints include the classical Darouach and Luenberger orders as special cases: the lower endpoint reduces to the Darouach order when $q_0=r$, while, under complete observability, the upper endpoint reduces to the Luenberger order $n-p$.
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