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

Noroozi, Navid; Mironchenko, Andrii; Kawan, Christoph und Zamani, Majid (2021): Set stability of infinite networks: ISS small-gain theory and its applications. In: Ifac Papersonline, Vol. 54, No. 9: pp. 72-77

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-tostate 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 smallgain theorem, we apply it to consensus of infinitely many agents, and to the design of distributed observers for infinite networks. Copyright (C) 2021 The Authors.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Computer Science
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science
• ISSN: 2405-8963
• Language: English