A networked small-gain theorem based on discrete-time diagonal stability
Abstract
We present a new sufficient condition for finite-gain input-to-output stability of a networked system. The condition requires a matrix, that combines information on the gains of the sub-systems and their interconnections, to be discrete-time diagonally stable (DTDS). We show that the new result generalizes the standard small gain theorem for the negative feedback connection of two sub-systems. An important advantage of the new result is that known sufficient conditions for DTDS can be applied to derive sufficient conditions for networked input-to-output stability. We demonstrate this using several examples. We also derive a new necessary and sufficient condition for a matrix that is a rank one perturbation of a Schur diagonal matrix to be DTDS.
Cite
@article{arxiv.2411.03380,
title = {A networked small-gain theorem based on discrete-time diagonal stability},
author = {Ron Ofir and Michael Margaliot},
journal= {arXiv preprint arXiv:2411.03380},
year = {2024}
}