Fixed-Time ISS for Interconnected Discrete-Time Systems, Part II: Finite-Horizon 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 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.
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: W7216544599