On Discrete-Time Polynomial Dynamical Systems on Hypergraphs

Shaoxuan Cui, Guofeng Zhang, Hildeberto Jardon-Kojakhmetov, Ming Cao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This letter studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron-Frobenius theorem for nonnegative tensors with respect to the tensors' Z-eigenvalues and Z-eigenvectors. Firstly, for a multilinear polynomial system on a uniform hypergraph, we study the stability of the origin of the corresponding systems. Next, we extend our results to non-homogeneous polynomial systems on non-uniform hypergraphs. We confirm that the local stability of any discrete-time polynomial system is in general dominated by pairwise terms. Assuming that the origin is locally stable, we construct a conservative (but explicit) region of attraction from the system parameters. Finally, we validate our results via some numerical examples.

Original languageEnglish
Pages (from-to)1078-1083
Number of pages6
JournalIEEE Control Systems Letters
Volume8
DOIs
Publication statusPublished - 2024

Keywords

  • Hypergraphs
  • Perron-Frobenius Theorem
  • Z-eigenvalues
  • higher-order interactions
  • polynomial systems
  • stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

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