  In this paper, stability of linearly coupled dynamical systems with feedback
pinning is studied. Event-triggered rules are employed on both diffusion
coupling and feedback pinning to reduce the updating load of the coupled
system. Here, both the coupling matrix and the set of pinned-nodes vary with
time are induced by a homogeneous Markov chain. For each node, the diffusion
coupling and feedback pinning are set up from the observation of its neighbors'
and target's (if pinned) information at the latest event time and the next
event time is triggered by some specified criteria. Two event-triggering rules
are proposed and it is proved that if the system with time-average coupling and
pinning gains are stable, the event-triggered strategies can stabilize the
system if the switching is sufficiently fast. Moreover, Zeno behaviors are
excluded in some cases. Finally, numerical examples are presented to illustrate
the theoretical results.
