Partitioned robustness analysis of networks with uncertain links

TL;DR

This paper introduces a new input-output model for networks with uncertain links, using integral quadratic constraints to ensure robust stability, with a focus on scalable and localized analysis through network partitioning.

Contribution

It develops a localized IQC-based framework for robust stability analysis of uncertain networks, balancing scalability and conservativeness.

Findings

The model effectively guarantees network stability under link uncertainties.

Partitioning allows scalable analysis with controllable conservativeness.

Numerical examples demonstrate the approach's practicality.

Abstract

An input-output model for networks with link uncertainty is developed. The main result presents a set of integral quadratic constraints (IQCs) that collectively imply robust stability of the uncertain network dynamics. The model dependency of each IQC is localized according to an edge-based partition of the network graph. The class of admissible network partitions affords scope for trading-off scalability against conservativeness. This is illustrated by numerical example.