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Attractivity Implies Lyapunov Stability for Multidimensional Fornasini--Marchesini Systems — arXiv:2611.09750

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.09750
License (as archived): CC0-1.0
Archived: 2026-11-09T22:42:35.857Z
SHA-256 of the archived text: 81033256c93a694c08a675427d0a9150881bd554cce11c0cbd90f80ed4b7b622
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How to cite

Attractivity Implies Lyapunov Stability for Multidimensional Fornasini--Marchesini Systems — arXiv:2611.09750 — arXiv (en), https://arxiv.org/abs/2611.09750 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_239abdca81ef (Metraipolis archive dc_239abdca81ef, sha256 81033256c93a694c08a675427d0a9150881bd554cce11c0cbd90f80ed4b7b622)

BibTeX

@misc{dc239abdca81ef,
  title = {Attractivity Implies Lyapunov Stability for Multidimensional Fornasini--Marchesini Systems — arXiv:2611.09750},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.09750},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_239abdca81ef; sha256 81033256c93a694c08a675427d0a9150881bd554cce11c0cbd90f80ed4b7b622},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.09750. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the linear multidimensional Fornasini--Marchesini recurrence with uniformly bounded boundary data prescribed on the open coordinate faces. Attractivity is understood in the sense of Pringsheim convergence, in which all discrete indices tend to infinity. We establish that attractivity alone implies Lyapunov stability, and consequently is equivalent to asymptotic stability, for an arbitrary number of discrete directions. Our proof combines inheritance of attractivity by lower-dimensional subsystems, a Baire-category uniform boundedness argument, and word-sum estimates to control coordinate slabs outside the Pringsheim tail. We use a generalized spectral stability criterion proved in a separate companion preprint, without reproving that criterion here. We also obtain a uniform exponential interior estimate and contrast our boundary/convergence convention with an earlier two-dimensional attractivity theorem.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2611.09750 — 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 2026-11-09T22:35:32.270Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).