Model reduction of synchronized homogeneous Lur'e networks with incrementally sector-bounded nonlinearities

Xiaodong Cheng (Corresponding author), Jacquelien M.A. Scherpen, Fan Zhang

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

This paper proposes a model order reduction scheme that reduces the complexity of diffusively coupled homogeneous Lur'e systems. We aim to reduce the dimension of each subsystem and meanwhile preserve the synchronization property of the overall network. Using the Laplacian spectral radius, we characterize the robust synchronization of the Lur'e network by a linear matrix inequality (LMI), whose solutions then are treated as generalized Gramians for the balanced truncation of the linear component of each Lur'e subsystem. It is verified that, with the same communication topology, the resulting reduced-order network system is still robustly synchronized, and an a priori bound on the approximation error is guaranteed to compare the behaviors of the full-order and reduced-order Lur'e subsystems.

LanguageEnglish
JournalEuropean Journal of Control
DOIs
StateE-pub ahead of print - 6 Jun 2019

Fingerprint

Synchronization
Linear matrix inequalities
Topology
Communication

Keywords

  • Balanced truncation
  • Lur'e system
  • Model reduction
  • Network synchronization

Cite this

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title = "Model reduction of synchronized homogeneous Lur'e networks with incrementally sector-bounded nonlinearities",
abstract = "This paper proposes a model order reduction scheme that reduces the complexity of diffusively coupled homogeneous Lur'e systems. We aim to reduce the dimension of each subsystem and meanwhile preserve the synchronization property of the overall network. Using the Laplacian spectral radius, we characterize the robust synchronization of the Lur'e network by a linear matrix inequality (LMI), whose solutions then are treated as generalized Gramians for the balanced truncation of the linear component of each Lur'e subsystem. It is verified that, with the same communication topology, the resulting reduced-order network system is still robustly synchronized, and an a priori bound on the approximation error is guaranteed to compare the behaviors of the full-order and reduced-order Lur'e subsystems.",
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Model reduction of synchronized homogeneous Lur'e networks with incrementally sector-bounded nonlinearities. / Cheng, Xiaodong (Corresponding author); Scherpen, Jacquelien M.A.; Zhang, Fan.

In: European Journal of Control, 06.06.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - This paper proposes a model order reduction scheme that reduces the complexity of diffusively coupled homogeneous Lur'e systems. We aim to reduce the dimension of each subsystem and meanwhile preserve the synchronization property of the overall network. Using the Laplacian spectral radius, we characterize the robust synchronization of the Lur'e network by a linear matrix inequality (LMI), whose solutions then are treated as generalized Gramians for the balanced truncation of the linear component of each Lur'e subsystem. It is verified that, with the same communication topology, the resulting reduced-order network system is still robustly synchronized, and an a priori bound on the approximation error is guaranteed to compare the behaviors of the full-order and reduced-order Lur'e subsystems.

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