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Non-conservative small-gain conditions for input-to-state stability with respect to not-necessarily compact sets

Title data

Noroozi, Navid ; Geiselhart, Roman ; Grüne, Lars ; Rüffer, Björn ; Wirth, Fabian:
Non-conservative small-gain conditions for input-to-state stability with respect to not-necessarily compact sets.
Passau , 2016 . - 16 p.

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Project information

Project title:
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Project's id
Humboldt Fellowship for Navid Noroozi
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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 the 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 not-necessarily compact sets. Toward this end, we first develop a Lyapunov characterization of ωISS via finite-step ωISS Lyapunov functions. Then, we provide the small-gain conditions to guarantee ωISS of a network of systems. Finally, applications of our results to partial input-to-state stability, ISS of time-varying systems, synchronization problems and decentralized observers are given.

Further data

Item Type: Preprint, postprint
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 > Chair 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: 14 Dec 2016 07:35
Last Modified: 14 Dec 2016 07:35
URI: https://eref.uni-bayreuth.de/id/eprint/35550

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