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arXiv · 1910.12746

A Lyapunov-based small-gain theorem for infinite networks

Christoph Kawan·Andrii Mironchenko·Abdalla Swikir·Navid Noroozi·Majid Zamani
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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.

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Christoph Kawan, Andrii Mironchenko, Abdalla Swikir, Navid Noroozi, Majid Zamani. 2019-10-28. A Lyapunov-based small-gain theorem for infinite networks. https://arxiv.org/abs/1910.12746

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