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A small-gain theorem for set stability of infinite networks : Distributed observation and ISS for time-varying networks

Title data

Noroozi, Navid ; Mironchenko, Andrii ; Kawan, Christoph ; Zamani, Majid:
A small-gain theorem for set stability of infinite networks : Distributed observation and ISS for time-varying networks.
In: European Journal of Control. Vol. 67 (2022) . - 100634.
ISSN 1435-5671
DOI: https://doi.org/10.1016/j.ejcon.2022.100634

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Abstract in another language

We generalize a small-gain theorem for a network of infinitely many systems, recently developed in [Kawan et. al, IEEE TAC (2021)]. The generalized small-gain theorem addresses exponential input-to-state stability with respect to closed sets, which enables us to study diverse control-theoretic problems in a unified manner, and it also allows for agents to have infinitely many neighbors. The small-gain condition, expressed in terms of the spectral radius of a gain operator collecting all the information about the internal Lyapunov gains, has several useful characterizations which simplify the verification of the condition. To demonstrate applicability of our small-gain theorem, we apply it to the stability analysis of infinite time-varying networks as well as the design of distributed observers for infinite networks.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: 9 pp.
Keywords: interconnected systems; input-to-state stability; small-gain theorem; Lyapunov methods
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 17 Mar 2025 09:19
Last Modified: 17 Mar 2025 09:19
URI: https://eref.uni-bayreuth.de/id/eprint/92852