Event-triggered stabilization of coupled dynamical systems with fast Markovian switching

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.