<p>Recently, the synchronization problem of variable-order fractional networks has garnered considerable attention. However, the intrinsic variability of the fractional order poses substantial challenges to convergence analysis, which hinders a rigorous and complete solution to the synchronization control. To address this, we investigate the passivity and bipartite synchronization of variable-order fractional spatio-temporal signed networks. Firstly, a new variable-order fractional integral inequality and a convergence result based on a variable-order fractional condition are developed, which provide a key theoretical foundation for adaptive control of variable-order systems. Furthermore, some pinning adaptive schemes are proposed, and sufficient criteria are derived for ensuring the passivity and bipartite synchronization, by decomposing the Laplacian matrix of the signed graph rather than the traditional gauge transformation. Finally, the validity of the proposed control schemes and derived criteria is demonstrated by numerical examples.</p>

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Adaptive pinning-based passivity and bipartite synchronization of fractional variable-order spatio-temporal signed networks

  • Lingbi Tang,
  • Cheng Hu,
  • Juan Yu,
  • Yu Sun,
  • Shiping Wen

摘要

Recently, the synchronization problem of variable-order fractional networks has garnered considerable attention. However, the intrinsic variability of the fractional order poses substantial challenges to convergence analysis, which hinders a rigorous and complete solution to the synchronization control. To address this, we investigate the passivity and bipartite synchronization of variable-order fractional spatio-temporal signed networks. Firstly, a new variable-order fractional integral inequality and a convergence result based on a variable-order fractional condition are developed, which provide a key theoretical foundation for adaptive control of variable-order systems. Furthermore, some pinning adaptive schemes are proposed, and sufficient criteria are derived for ensuring the passivity and bipartite synchronization, by decomposing the Laplacian matrix of the signed graph rather than the traditional gauge transformation. Finally, the validity of the proposed control schemes and derived criteria is demonstrated by numerical examples.