A Lyapunov-based small-gain theorem for infinite networks
Optimization and Control
2020-12-02 v3
Abstract
This paper 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.
Cite
@article{arxiv.1910.12746,
title = {A Lyapunov-based small-gain theorem for infinite networks},
author = {Christoph Kawan and Andrii Mironchenko and Abdalla Swikir and Navid Noroozi and Majid Zamani},
journal= {arXiv preprint arXiv:1910.12746},
year = {2020}
}