  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.
