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ISS and integral ISS coincide for linear systems with bounded inputs

  • Sahiba Arora
  • Philip Preußler
  • Felix Schwenninger
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Abstract

We show that input-to-state stability (ISS) and integral input-to-state stability (integral ISS) with respect to the space of essentially bounded functions are equivalent properties for linear systems. The proof combines recent results on Orlicz-admissibility and a duality result due to the authors. As a direct consequence, we show that, given an L∞-admissible control operator, the mild solutions of the linear system are continuous, resolving a question by G.\ Weiss.

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Cite

BibTeXRIS
BibTeX
@misc{arora2026integral,
  title = {{ISS and integral ISS coincide for linear systems with bounded inputs}},
  author = {Sahiba Arora and Philip Preußler and Felix Schwenninger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40348},
  eprint = {2609.40348},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40348},
}
RIS
TY  - UNPB
TI  - ISS and integral ISS coincide for linear systems with bounded inputs
AU  - Sahiba Arora
AU  - Philip Preußler
AU  - Felix Schwenninger
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40348
UR  - https://arxiv.org/abs/2609.40348
AB  - We show that input-to-state stability (ISS) and integral input-to-state stability (integral ISS) with respect to the space of essentially bounded functions are equivalent properties for linear systems. The proof combines recent results on Orlicz-admissibility and a duality result due to the authors. As a direct consequence, we show that, given an L^∞-admissible control operator, the mild solutions of the linear system are continuous, resolving a question by G.\ Weiss.
ER  -