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PreprintCC BY 4.0arXiv

Fixed-Time ISS for Interconnected Discrete-Time Systems, Part II: Finite-Horizon 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 using finite-horizon Lyapunov functions. In the proposed Lyapunov- based characterization, the effect of the initial condition is eliminated after a uniformly bounded number of iterations. This characterization encompasses existing extinction-based Lyapunov conditions while allowing more general finite-memory mechanisms. Building on this framework, we establish a finite-horizon small-gain theorem for interconnected discrete-time systems, providing conditions under which FxT-ISS is preserved under feedback interconnections. The proposed framework is illustrated through examples arising in distributed algorithms, optimization, and feedback optimization.

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Cite

BibTeXRIS
BibTeX
@misc{rubaiyat2026fixedtime,
  title = {{Fixed-Time ISS for Interconnected Discrete-Time Systems, Part II: Finite-Horizon Lyapunov Functions}},
  author = {Sumadhu Rubaiyat and Jorge I. Poveda},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00660},
  eprint = {2610.00660},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00660},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fixed-Time ISS for Interconnected Discrete-Time Systems, Part II: Finite-Horizon Lyapunov Functions
AU  - Sumadhu Rubaiyat
AU  - Jorge I. Poveda
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.00660
UR  - https://arxiv.org/abs/2610.00660
AB  - We study fixed-time input-to-state stability (FxT-ISS) for discrete-time systems subject to exogenous inputs using finite-horizon Lyapunov functions. In the proposed Lyapunov- based characterization, the effect of the initial condition is eliminated after a uniformly bounded number of iterations. This characterization encompasses existing extinction-based Lyapunov conditions while allowing more general finite-memory mechanisms. Building on this framework, we establish a finite-horizon small-gain theorem for interconnected discrete-time systems, providing conditions under which FxT-ISS is preserved under feedback interconnections. The proposed framework is illustrated through examples arising in distributed algorithms, optimization, and feedback optimization.
ER  -