Fixed-Time ISS for Interconnected Discrete-Time Systems, Part I: Extinction-Based Lyapunov Functions
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Rubaiyat, Sumadhu, Poveda, Jorge I.
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216129127