功能特性线性系统统一特征值-特征子空间准则及广义分离原理
Unified Eigenvalue-Eigenspace Criteria for Functional Properties of Linear Systems and the Generalized Separation Principle
AI总结：
本文提出功能特性线性系统统一特征值-特征子空间准则，引入内在功能可控性和镇定性概念，实现功能层面的广义分离原理。
摘要：
经典可控性和可观测性刻画了完整系统状态的可达性和可重构性，并允许等价的几何和基于特征值的Popov-Belevitch-Hautus（PBH）测试。受大规模和网络化系统中只关心选定状态线性组合的启发，本文研究这些性质的功能扩展。开发了一种PBH风格的框架用于功能系统性质，提供必要的和充分的谱特征刻画。结果适用于可对角化和不可对角化的系统，并恢复经典PBH测试作为特殊情况。引入了两个新的内在概念：内在功能可控性和内在功能镇定性。这些内在性质直接以与功能相关的不变子空间形式提出，为功能控制器设计和基于观测器的功能控制器设计所需的可接受增强存在性提供可验证条件。内在框架在功能层面实现了广义分离原理，确立功能控制器和功能观测器可以独立设计。示例说明了理论并突显了在缺乏完整状态可控性或可观测性的情况下，功能控制和估计可能存在的状况。
英文摘要：
Classical controllability and observability admit equivalent Popov-Belevitch-Hautus (PBH) tests based on eigenvalue-wise rank conditions. This paper extends this framework to functional properties of linear systems, establishing necessary and sufficient PBH-style conditions for Functional Controllability, Functional Stabilizability, Functional Observability, and Functional Detectability in terms of generalized eigenspaces. By contrast, Target Output Controllability is shown not to admit an independent eigenvalue-wise characterization in general; a necessary and sufficient eigenstructure condition is derived instead. We further introduce Intrinsic Functional Controllability and Intrinsic Functional Stabilizability, which give necessary and sufficient conditions for the existence of the augmentation matrices required for functional controller and observer synthesis. These intrinsic properties yield a Generalized Separation Principle that recovers the classical separation principle as a special case.
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