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PreprintCC BY 4.0arXiv

Fixed-Time ISS for Interconnected Discrete-Time Systems, Part I: Extinction-Based Lyapunov Functions

  • Sumadhu Rubaiyat
  • Jorge I. Poveda
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Abstract

We study fixed-time input-to-state stability (FxT-ISS) for discrete-time systems subject to exogenous inputs. We introduce Lyapunov-based sufficient conditions for FxT- ISS based on a class of dissipation functions with a fixed-time extinction property, which encompasses commonly used two- power constructions while allowing substantially more general decay mechanisms. Building on this framework, we establish a small-gain theorem for interconnected FxT-ISS systems in the presence of disturbances. The results are illustrated through several examples, including perturbed optimization algorithms and a discrete-time feedback-optimization architecture.

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Cite

BibTeXRIS
BibTeX
@misc{rubaiyat2026fixedtime,
  title = {{Fixed-Time ISS for Interconnected Discrete-Time Systems, Part I: Extinction-Based Lyapunov Functions}},
  author = {Sumadhu Rubaiyat and Jorge I. Poveda},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00657},
  eprint = {2610.00657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00657},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fixed-Time ISS for Interconnected Discrete-Time Systems, Part I: Extinction-Based Lyapunov Functions
AU  - Sumadhu Rubaiyat
AU  - Jorge I. Poveda
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00657
UR  - https://arxiv.org/abs/2610.00657
AB  - We study fixed-time input-to-state stability (FxT-ISS) for discrete-time systems subject to exogenous inputs. We introduce Lyapunov-based sufficient conditions for FxT- ISS based on a class of dissipation functions with a fixed-time extinction property, which encompasses commonly used two- power constructions while allowing substantially more general decay mechanisms. Building on this framework, we establish a small-gain theorem for interconnected FxT-ISS systems in the presence of disturbances. The results are illustrated through several examples, including perturbed optimization algorithms and a discrete-time feedback-optimization architecture.
ER  -