  The issue of cyber-security has become ever more prevalent in the analysis
and design of cyber-physical systems. In this paper, we investigate
self-triggered consensus networks in the presence of communication failures
caused by Denialof- Service (DoS) attacks. A general framework is considered in
which the network links can fail independent of each other. By introducing a
notion of Persistency-of-Communication (PoC), we provide an explicit
characterization of DoS frequency and duration under which consensus can be
preserved by suitably designing time-varying control and communication
policies. An explicit characterization of the effects of DoS on the consensus
time is also provided. The considered notion of PoC is compared with classic
average connectivity conditions that are found in pure continuous-time
consensus networks. Finally, examples are given to substantiate the analysis.
