Set stability of infinite networks : ISS small-gain theory and its applications

Titelangaben

Noroozi, Navid ; Mironchenko, Andrii ; Kawan, Christoph ; Zamani, Majid:
Set stability of infinite networks : ISS small-gain theory and its applications.
In: IFAC-PapersOnLine. Bd. 54 (2021) Heft 9 . - S. 72-77.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2021.06.063

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Abstract

Motivated by a paradigm shift towards a hyper-connected world, we develop a computationally tractable small-gain theorem for networks of infinitely many subsystems, termed as infinite networks. The proposed small-gain theorem addresses exponential input-to-state stability with respect to closed sets, which enables us to analyze diverse stability problems in a unified manner. The small-gain condition, expressed in terms of the spectral radius of a gain operator collecting all the information about the internal Lyapunov gains, can be numerically checked efficiently for a large class of systems. To demonstrate broad applicability of our small-gain theorem, we apply it to consensus of infinitely many agents, and to the design of distributed observers for infinite networks.