Iterative Algorithms for Assessing Network Resilience Against Structured Perturbations

TL;DR

This paper introduces iterative algorithms to evaluate network resilience against structured perturbations, providing tools to measure worst-case destabilization and maximum tolerable perturbation energy in linear time-invariant networks.

Contribution

It presents novel iterative methods with theoretical convergence guarantees for computing structured pseudospectral abscissa and stability radius in network systems.

Findings

Algorithms efficiently compute worst-case perturbations.

Methods accurately assess network stability margins.

Validated on multiple network examples.

Abstract

This paper studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity and entry-wise constraints. Given an energy level, the structured pseudospectral abscissa captures the worst-possible perturbation an adversary could employ to de-stabilize the network, and the structured stability radius is the maximum energy in the structured perturbation that the network can withstand without becoming unstable. Building on a novel characterization of the worst-case structured perturbation, we propose iterative algorithms that efficiently compute the structured pseudospectral abscissa and structured stability radius. We provide theoretical guarantees of the local convergence of the algorithms and illustrate their efficacy and accuracy on several network examples.