A. Mironchenko. A spectral small-gain condition for input-to-state stability of infinite networks

Title: A spectral small-gain condition for input-to-state stability of infinite networks

Link to journal version of the paper (preprint):

Talk at IFAC WC 2020 in Berlin, Germany

Slides:

Abstract of the paper:
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.