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A Lyapunov-Based Small-Gain Theorem for Infinite Networks | IEEE Journals & Magazine | IEEE Xplore

A Lyapunov-Based Small-Gain Theorem for Infinite Networks


Abstract:

This article presents a small-gain theorem for networks composed of a countably infinite number of finite-dimensional subsystems. Assuming that each subsystem is exponent...Show More

Abstract:

This article 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.
Published in: IEEE Transactions on Automatic Control ( Volume: 66, Issue: 12, December 2021)
Page(s): 5830 - 5844
Date of Publication: 03 December 2020

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