Title data
Noroozi, Navid ; Geiselhart, Roman ; Grüne, Lars ; Rüffer, Björn ; Wirth, Fabian:
Nonconservative discretetime ISS smallgain conditions for closed sets.
In: IEEE Transactions on Automatic Control.
Vol. 63
(2018)
Issue 5
.
 pp. 12311242.
ISSN 00189286
DOI: https://doi.org/10.1109/TAC.2017.2735194
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Project financing: 
Alexander von HumboldtStiftung 
Abstract in another language
This paper presents a unification and a generalization of the smallgain theory subsuming a wide range of existing smallgain theorems. In particular, we introduce smallgain conditions that are necessary and sufficient to ensure inputtostate stability (ISS) with respect to closed sets. Toward this end, we first develop a Lyapunov characterization of ω ISS via finitestep ω ISS Lyapunov functions. Then, we provide the smallgain conditions to guarantee ωISS of a network of systems. Finally, applications of our results to partial ISS, ISS of timevarying systems, synchronization problems, incremental stability, and distributed observers are given.
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Nonconservative smallgain conditions for inputtostate stability with respect to notnecessarily compact sets. (deposited 14 Dec 2016 07:35)
 Nonconservative discretetime ISS smallgain conditions for closed sets. (deposited 08 Aug 2017 06:20) [Currently Displayed]