A spectral small-gain condition for input-to-state stability of infinite networks. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Kawan, Christoph; Mironchenko, Andrii; Swikir, Abdalla; Noroozi, Navid; Zamani, Majid
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 5303
• Page End: 5308
• Publication Date: 2020
• Subjects: Nonlinear systems -- small-gain theorems -- infinite-dimensional systems -- input-to-state stability -- Lyapunov methods -- large-scale systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.1214
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper presents a tight small-gain theorem for networks composed of infinitely many 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. We illustrate the effectiveness of our result by applying it to traffic networks.