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

Sumadhu Rubaiyat; Jorge I. Poveda

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arXiv · 2610.00657

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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BibTeX RIS

Sumadhu Rubaiyat, Jorge I. Poveda. 2026-09-30. Fixed-Time ISS for Interconnected Discrete-Time Systems, Part I: Extinction-Based Lyapunov Functions. https://arxiv.org/abs/2610.00657

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