  Resilience of cyber-physical networks to unexpected failures is a critical
need widely recognized across domains. For instance, power grids,
telecommunication networks, transportation infrastructures and water treatment
systems have all been subject to disruptive malfunctions and catastrophic
cyber-attacks. Following such adverse events, we investigate scenarios where a
node of a linear network suffers a loss of control authority over some of its
actuators. These actuators are not following the controller's commands and are
instead producing undesirable outputs. The repercussions of such a loss of
control can propagate and destabilize the whole network despite the malfunction
occurring at a single node. To assess system vulnerability, we establish
resilience conditions for networks with a subsystem enduring a loss of control
authority over some of its actuators. Furthermore, we quantify the
destabilizing impact on the overall network when such a malfunction perturbs a
nonresilient subsystem. We illustrate our resilience conditions on two academic
examples, on an islanded microgrid, and on the linearized IEEE 39-bus system.
