Non-conservative discrete-time ISS small-gain conditions for closed sets
Optimization and Control
2017-08-22 v2
Abstract
This paper presents a unification and a generalization of the small-gain theory subsuming a wide range of existing small-gain theorems. In particular, we introduce small-gain conditions that are necessary and sufficient to ensure input-to-state stability (ISS) with respect to closed sets. Toward this end, we first develop a Lyapunov characterization of ISS via finite-step ISS Lyapunov functions. Then, we provide the small-gain conditions to guarantee ISS of a network of systems. Finally, applications of our results to partial input-to-state stability, ISS of time-varying systems, synchronization problems, incremental stability, and distributed observers are given.
Keywords
Cite
@article{arxiv.1612.03710,
title = {Non-conservative discrete-time ISS small-gain conditions for closed sets},
author = {Navid Noroozi and Roman Geiselhart and Lars Grüne and Björn S. Rüffer and Fabian R. Wirth},
journal= {arXiv preprint arXiv:1612.03710},
year = {2017}
}