On the Popov–Belevitch–Hautus tests for functional observability and output controllability

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Automatica Pub Date : 2025-04-01 Epub Date: 2025-01-24 DOI:10.1016/j.automatica.2025.112122

Arthur N. Montanari , Chao Duan , Adilson E. Motter

引用次数: 0

Abstract

Functional observability and output controllability are properties that establish the conditions for the partial estimation and partial control of the system state, respectively. In the special case of full-state observability and controllability, the Popov–Belevitch–Hautus (PBH) tests provide conditions for the properties to hold based on the system eigenspace. Generalizations of the PBH tests have been recently proposed for functional observability and output controllability, but thus far they have only been proven valid for diagonalizable systems. Here, we rigorously establish the generalized PBH test for functional observability, extending its validity to a broader class of systems using Jordan decomposition. Likewise, we determine the class of systems under which the generalized PBH test is sufficient and necessary for output controllability. These results have immediate implications for observer and controller design, pole assignment, and optimal placement of sensors and drivers.

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关于功能可观察性和输出可控性的Popov-Belevitch-Hautus检验

函数的可观测性和输出的可控性分别为系统状态的部分估计和部分控制建立了条件。在全态可见性和可控性的特殊情况下，基于系统特征空间的Popov-Belevitch-Hautus （PBH）检验提供了这些性质保持的条件。最近提出了对功能可观察性和输出可控性的PBH测试的推广，但到目前为止，它们仅被证明对可对角化系统有效。在这里，我们严格地建立了广义PBH检验的功能可观察性，将其有效性扩展到更广泛的一类系统使用约旦分解。同样地，我们确定了一类系统，在这些系统下，广义PBH检验对于输出可控性是充分和必要的。这些结果对观测器和控制器设计、极点配置以及传感器和驱动器的最佳放置具有直接意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.

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