A spectral small-gain condition for input-to-state stability of infinite networks. Issue 2 (2020) - Kawan, Christoph; Mironchenko, Andrii; Swikir, Abdalla; Noroozi, Navid; Zamani, Majid
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.