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

Title data

Noroozi, Navid ; Geiselhart, Roman ; Grüne, Lars ; Rüffer, Björn ; Wirth, Fabian:
Non-conservative discrete-time ISS small-gain conditions for closed sets.
In: IEEE Transactions on Automatic Control. Vol. 63 (2018) Issue 5 . - pp. 1231-1242.
ISSN 0018-9286
DOI: https://doi.org/10.1109/TAC.2017.2735194

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Project's official titleProject's id
Humboldt Fellowship for Navid NorooziNo information

Project financing: Alexander von Humboldt-Stiftung

Abstract in another language

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 ωISS of a network of systems. Finally, applications of our results to partial ISS, ISS of time-varying systems, synchronization problems, incremental stability, and distributed observers are given.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: large-scale discrete-time systems; Lyapunov methods; input-to-state stability
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 08 Aug 2017 06:20
Last Modified: 26 Apr 2018 08:43
URI: https://eref.uni-bayreuth.de/id/eprint/39076

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