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

Titelangaben

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. Bd. 67 (2022) . - 100634.
ISSN 1435-5671
DOI: https://doi.org/10.1016/j.ejcon.2022.100634

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Abstract

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.