Skip to content
DraconiticResearch
Search Sources API
182,469 studies31 sourcesUpdated 15 min ago
PreprintarXiv licencearXiv

BIBO stability in infinite dimensions: extensions and limitations of finite-dimensional theory

  • Sahiba Arora
  • Alexander A. Wierzba
Open at sourcePDFDOICite

Abstract

The study of bounded-input bounded-output (BIBO) stability of infinite-dimensional systems gives rise to difficulties that do not occur in the classical finite-dimensional setting. In this paper, we resolve several questions concerning the definition and characterisation of BIBO stability in the framework of system nodes. In particular, we show that C∞-BIBO stability need not imply L∞-BIBO stability in general, but that the two notions are equivalent when the output space is reflexive. Furthermore, we investigate to what extent classical results extend to the infinite-dimensional setting, including the relation between BIBO stability and exponential stability under controllability and observability assumptions.

Related

  1. Infinite-order p-adic differential equations for Hurwitz-type Euler zeta functions: Uniqueness and higher-dimensional extensions
    Su Hu, Min-Soo Kim
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  2. On the Stability Analysis of Infinite-Dimensional Port-Hamiltonian Systems Within the Variational Framework
    Moritz Leitner, Lukas Ecker, Markus Schöberl
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  3. Sampling with Autoregressive Clock Jitter: Infinite-Dimensional Stability Failure and Finite-Dimensional Conditioning
    Daniele Gerosa, Thomas Eriksson
    arXivPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsarXiv
  4. A note on purely infinite extensions
    Ping Wong Ng, Cangyuan Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Discrete C*-Frobenius Algebras and Infinite-Index Extensions in Algebraic Quantum Field Theories
    Ziyun Xu
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{arora2026bibo,
  title = {{BIBO stability in infinite dimensions: extensions and limitations of finite-dimensional theory}},
  author = {Sahiba Arora and Alexander A. Wierzba},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27138},
  eprint = {2610.27138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27138},
}
RIS
TY  - UNPB
TI  - BIBO stability in infinite dimensions: extensions and limitations of finite-dimensional theory
AU  - Sahiba Arora
AU  - Alexander A. Wierzba
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27138
UR  - https://arxiv.org/abs/2610.27138
AB  - The study of bounded-input bounded-output (BIBO) stability of infinite-dimensional systems gives rise to difficulties that do not occur in the classical finite-dimensional setting. In this paper, we resolve several questions concerning the definition and characterisation of BIBO stability in the framework of system nodes. In particular, we show that C^∞-BIBO stability need not imply L^∞-BIBO stability in general, but that the two notions are equivalent when the output space is reflexive. Furthermore, we investigate to what extent classical results extend to the infinite-dimensional setting, including the relation between BIBO stability and exponential stability under controllability and observability assumptions.
ER  -