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Consensusability of Continuous-Time Multi-Agent Systems With Unbounded Heterogeneous Constant Delays: A Signed Laplacian Perspective — arXiv:2608.15133

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.15133
License (as archived): CC0-1.0
Archived: 2026-10-18T20:15:14.811Z
SHA-256 of the archived text: b862a8855cdba2b88e8533add9a7ab3a0b8f9ec5e7fa3255bad3e63a72875efc
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How to cite

Consensusability of Continuous-Time Multi-Agent Systems With Unbounded Heterogeneous Constant Delays: A Signed Laplacian Perspective — arXiv:2608.15133 — arXiv (en), https://arxiv.org/abs/2608.15133 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b95f623aa9fd (Metraipolis archive dc_b95f623aa9fd, sha256 b862a8855cdba2b88e8533add9a7ab3a0b8f9ec5e7fa3255bad3e63a72875efc)

BibTeX

@misc{dcb95f623aa9fd,
  title = {Consensusability of Continuous-Time Multi-Agent Systems With Unbounded Heterogeneous Constant Delays: A Signed Laplacian Perspective — arXiv:2608.15133},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.15133},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b95f623aa9fd; sha256 b862a8855cdba2b88e8533add9a7ab3a0b8f9ec5e7fa3255bad3e63a72875efc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.15133. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The consensus of continuous-time multi-agent systems with unbounded and heterogeneous constant delays is investigated by combining frequency-domain analysis and algebraic graph theory. Several types of signed Laplacians are constructed to characterize consensusability under delays. The core results are established based on the defined delay-embedded signed Laplacian, where a small-delay link creates a cooperative interaction and a possibly unbounded large-delay link creates an antagonistic interaction between the agents. The dividing line between small and large delays is given by $\tau_{ij}=\pi/2\lambda_{\max}(L_0)$, where $\lambda_{\max}(L_0)$ refers to the maximum eigenvalue of the conventional graph Laplacian. It is proved that the consensusability is preserved if the delay-embedded signed Laplacian is positive semi-definite with a simple zero eigenvalue. Moreover, we derived some consensus conditions in terms of the extended effective resistance which measures the overall coupling between two sets of agents. The obtained results provide new insights into the mechanism of delayed consensus from the interplay between the small-delay-induced cooperativeness and large-delay-induced antagonism in the underlying network topology.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-18 in math.OC).
Categorie arXiv: Optimization and Control (math.OC) ; Systems and Control (eess.SY); Dynamical Systems (math.DS).
Pagina del lavoro: https://arxiv.org/abs/2608.15133 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T19:45:07.837Z dalla pagina https://arxiv.org/catchup/math.OC/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).