Neighbourhood conditions for network stability with link uncertainty

TL;DR

This paper develops decentralized stability conditions for networks with uncertain links, leveraging neighborhood-based integral quadratic constraints to improve robustness analysis over traditional link-wise methods.

Contribution

It introduces a novel neighborhood-based integral quadratic constraint framework for structured robust stability analysis of uncertain networked systems.

Findings

Neighborhood conditions outperform link-wise conditions in robustness.

Numerical example demonstrates broader applicability and less conservatism.

Conditions are decentralized, relying on local neighborhood data.

Abstract

The main result relates to structured robust stability analysis of an input-output model for networks with link uncertainty. It constitutes a collection of integral quadratic constraints, which together imply robust stability of the uncertain networked dynamics. Each condition is decentralized in the sense that it depends on model data pertaining to the neighbourhood of a specific agent. By contrast, pre-existing conditions for the network model are link-wise decentralized, with each involving conservatively more localized problem data. A numerical example is presented to illustrate the advantage of the new broader neighbourhood conditions.