Trajectory-Based Region of Attraction Estimation on Higher-Order Networked Nonlinear Systems

Jin Zhou; Haoran Liu; Shuaibing Zhu; Jun An Lu; Jinhu Lu

doi:10.1109/LCSYS.2026.3659802

Trajectory-Based Region of Attraction Estimation on Higher-Order Networked Nonlinear Systems

Jin Zhou
, Haoran Liu^*
, Shuaibing Zhu
, Jun An Lu
, Jinhu Lu

^*Corresponding author for this work

School of Automation Science and Electrical Engineering

Wuhan University
Hunan Normal University

Research output: Contribution to journal › Article › peer-review

Abstract

This letter presents a theoretical framework for estimating the trajectory-based region of attraction in nonlinear higher-order networks. A Lyapunov-based criterion is established for time-varying systems to determine the domain in which all trajectories converge to a reference trajectory. The result is expressed as a spherical region characterized by parameters of the linearized dynamics. Two corollaries admit closed-form and eigenmode-based estimations, respectively enabling a direct region radius calculation and reducing system dimension significantly. Numerical simulations on a higher-order network of forced pendulums validate the proposed analysis and demonstrate its accuracy and efficiency.

Original language	English
Pages (from-to)	73-78
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	10
DOIs	https://doi.org/10.1109/LCSYS.2026.3659802
State	Published - 2026

Keywords

Lyapunov methods
network analysis and control
time-varying systems

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10.1109/LCSYS.2026.3659802

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title = "Trajectory-Based Region of Attraction Estimation on Higher-Order Networked Nonlinear Systems",

abstract = "This letter presents a theoretical framework for estimating the trajectory-based region of attraction in nonlinear higher-order networks. A Lyapunov-based criterion is established for time-varying systems to determine the domain in which all trajectories converge to a reference trajectory. The result is expressed as a spherical region characterized by parameters of the linearized dynamics. Two corollaries admit closed-form and eigenmode-based estimations, respectively enabling a direct region radius calculation and reducing system dimension significantly. Numerical simulations on a higher-order network of forced pendulums validate the proposed analysis and demonstrate its accuracy and efficiency.",

keywords = "Lyapunov methods, network analysis and control, time-varying systems",

author = "Jin Zhou and Haoran Liu and Shuaibing Zhu and Lu, \{Jun An\} and Jinhu Lu",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",

year = "2026",

doi = "10.1109/LCSYS.2026.3659802",

language = "英语",

volume = "10",

pages = "73--78",

journal = "IEEE Control Systems Letters",

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T1 - Trajectory-Based Region of Attraction Estimation on Higher-Order Networked Nonlinear Systems

AU - Zhou, Jin

AU - Liu, Haoran

AU - Zhu, Shuaibing

AU - Lu, Jun An

AU - Lu, Jinhu

PY - 2026

Y1 - 2026

N2 - This letter presents a theoretical framework for estimating the trajectory-based region of attraction in nonlinear higher-order networks. A Lyapunov-based criterion is established for time-varying systems to determine the domain in which all trajectories converge to a reference trajectory. The result is expressed as a spherical region characterized by parameters of the linearized dynamics. Two corollaries admit closed-form and eigenmode-based estimations, respectively enabling a direct region radius calculation and reducing system dimension significantly. Numerical simulations on a higher-order network of forced pendulums validate the proposed analysis and demonstrate its accuracy and efficiency.

AB - This letter presents a theoretical framework for estimating the trajectory-based region of attraction in nonlinear higher-order networks. A Lyapunov-based criterion is established for time-varying systems to determine the domain in which all trajectories converge to a reference trajectory. The result is expressed as a spherical region characterized by parameters of the linearized dynamics. Two corollaries admit closed-form and eigenmode-based estimations, respectively enabling a direct region radius calculation and reducing system dimension significantly. Numerical simulations on a higher-order network of forced pendulums validate the proposed analysis and demonstrate its accuracy and efficiency.

KW - Lyapunov methods

KW - network analysis and control

KW - time-varying systems

UR - https://www.scopus.com/pages/publications/105029098361

U2 - 10.1109/LCSYS.2026.3659802

DO - 10.1109/LCSYS.2026.3659802

M3 - 文章

AN - SCOPUS:105029098361

SN - 2475-1456

VL - 10

SP - 73

EP - 78

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -

Trajectory-Based Region of Attraction Estimation on Higher-Order Networked Nonlinear Systems

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Keywords

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