A note on structural controllability and observability indices

Yuan Zhang; Ranbo Cheng; Ziyuan Luo; Yuanqing Xia

doi:10.1016/j.automatica.2025.112675

A note on structural controllability and observability indices

Yuan Zhang
, Ranbo Cheng
, Ziyuan Luo
, Yuanqing Xia^*

^*此作品的通讯作者

Beijing Institute of Technology
Zhongyuan University of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this note, we investigate the structural controllability and observability indices of structured systems. We provide counter-examples showing that an existing graph-theoretic characterization for the structural controllability index (SCOI) may not hold, even for systems with self-loop at every state node. We further demonstrate that this characterization actually provides upper bounds, and extend them to new graph-theoretic characterizations applicable to structurally uncontrollable systems. Additionally, we reveal that an existing method may fail to obtain the exact SCOI. Consequently, complete graph-theoretic characterizations and polynomial-time computation of SCOI remain open. Given this, we present an efficiently computable tight lower bound, whose tightness is validated by numerical simulations. All these results apply to the structural observability index by the duality between controllability and observability.

源语言	英语
文章编号	112675
期刊	Automatica
卷	183
DOI	https://doi.org/10.1016/j.automatica.2025.112675
出版状态	已出版 - 1月 2026
已对外发布	是

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abstract = "In this note, we investigate the structural controllability and observability indices of structured systems. We provide counter-examples showing that an existing graph-theoretic characterization for the structural controllability index (SCOI) may not hold, even for systems with self-loop at every state node. We further demonstrate that this characterization actually provides upper bounds, and extend them to new graph-theoretic characterizations applicable to structurally uncontrollable systems. Additionally, we reveal that an existing method may fail to obtain the exact SCOI. Consequently, complete graph-theoretic characterizations and polynomial-time computation of SCOI remain open. Given this, we present an efficiently computable tight lower bound, whose tightness is validated by numerical simulations. All these results apply to the structural observability index by the duality between controllability and observability.",

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AU - Zhang, Yuan

AU - Cheng, Ranbo

AU - Luo, Ziyuan

AU - Xia, Yuanqing

PY - 2026/1

Y1 - 2026/1

N2 - In this note, we investigate the structural controllability and observability indices of structured systems. We provide counter-examples showing that an existing graph-theoretic characterization for the structural controllability index (SCOI) may not hold, even for systems with self-loop at every state node. We further demonstrate that this characterization actually provides upper bounds, and extend them to new graph-theoretic characterizations applicable to structurally uncontrollable systems. Additionally, we reveal that an existing method may fail to obtain the exact SCOI. Consequently, complete graph-theoretic characterizations and polynomial-time computation of SCOI remain open. Given this, we present an efficiently computable tight lower bound, whose tightness is validated by numerical simulations. All these results apply to the structural observability index by the duality between controllability and observability.

AB - In this note, we investigate the structural controllability and observability indices of structured systems. We provide counter-examples showing that an existing graph-theoretic characterization for the structural controllability index (SCOI) may not hold, even for systems with self-loop at every state node. We further demonstrate that this characterization actually provides upper bounds, and extend them to new graph-theoretic characterizations applicable to structurally uncontrollable systems. Additionally, we reveal that an existing method may fail to obtain the exact SCOI. Consequently, complete graph-theoretic characterizations and polynomial-time computation of SCOI remain open. Given this, we present an efficiently computable tight lower bound, whose tightness is validated by numerical simulations. All these results apply to the structural observability index by the duality between controllability and observability.

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VL - 183

JO - Automatica

JF - Automatica

M1 - 112675

ER -

A note on structural controllability and observability indices

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