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arXiv · 2610.00660

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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Sumadhu Rubaiyat, Jorge I. Poveda. 2026-09-30. Fixed-Time ISS for Interconnected Discrete-Time Systems, Part II: Finite-Horizon Lyapunov Functions. https://arxiv.org/abs/2610.00660

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