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arXiv · 1612.03710

Non-conservative discrete-time ISS small-gain conditions for closed sets

Navid Noroozi·Roman Geiselhart·Lars Grüne·Björn S. Rüffer·Fabian R. Wirth
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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 $ω$ISS via finite-step $ω$ISS Lyapunov functions. Then, we provide the small-gain conditions to guarantee $ω$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.

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Navid Noroozi, Roman Geiselhart, Lars Grüne, Björn S. Rüffer, Fabian R. Wirth. 2017-08-21. Non-conservative discrete-time ISS small-gain conditions for closed sets. https://arxiv.org/abs/1612.03710

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