A Lyapunov-Based Small-Gain Theorem for Infinite Networks

Kawan, Christoph; Mironchenko, Andrii; Swikir, Abdalla; Noroozi, Navid und Zamani, Majid (2021): A Lyapunov-Based Small-Gain Theorem for Infinite Networks. In: IEEE Transactions on Automatic Control, Bd. 66, Nr. 12: S. 5830-5844

Abstract

This article presents a small-gain theorem for networks composed of a countably infinite number of finite-dimensional subsystems. Assuming that each subsystem is exponentially input-to-state stable, we show that if the gain operator, collecting all the information about the internal Lyapunov gains, has a spectral radius less than one, the overall infinite network is exponentially input-to-state stable. The effectiveness of our result is illustrated through several examples including nonlinear spatially invariant systems with sector nonlinearities and a road traffic network.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0018-9286
• Sprache: Englisch