  We investigate the disruption of discrete-time consensus problems via
grounding. Loosely speaking, grounding a network occurs if the state of one
agent no longer responds to inputs from other agents and/or changes its
dynamics. Then, the agent becomes a leader or a so-called stubborn agent. The
disruption of the agent can be caused by internal faults, safety protocols or
due to an external malicious attack. In this paper we investigate how grounding
affects expander graph families that usually exhibit good scaling properties
with increasing network size. It is shown that the algebraic connectivity and
eigenratio of the network decrease due to the grounding causing the performance
and scalability of the network to deteriorate, even to the point of losing
consensusability. We then present possible countermeasures to such disruptions
and discuss their practicality and limitations. In particular, for a specific
countermeasure of deliberately grounding additional nodes, we investigate
extensively how to select additional nodes to ground and how many nodes we need
to ground to recover the consensus performance. Our findings are supported by a
wide range of numerical simulations.
