  This paper studies the synchronization of stochastic linear systems which are
subject to a general class of noises, in the sense that the noises are bounded
in covariance but might be correlated with the states of agents and among each
other. We propose an event-based control protocol for achieving the
synchronization among agents in the mean square sense and theoretically analyze
the performance of it by using a stochastic Lyapunov function, where the
stability of $c$-martingales is particularly developed to handle the challenges
brought by the general model of noises and the event-triggering mechanism. The
proposed event-based synchronization algorithm is then applied to solve the
problem of distributed estimation in sensor network. Specifically, by
losslessly decomposing the optimal Kalman filter, it is shown that the problem
of distributed estimation can be resolved by using the algorithms designed for
achieving the synchronization of stochastic linear systems. As such, an
event-based distributed estimation algorithm is developed, where each sensor
performs local filtering solely using its own measurement, together with the
proposed event-based synchronization algorithm to fuse the local estimates of
neighboring nodes. With the reduced communication frequency, the designed
estimator is proved to be stable under the minimal requirements of network
connectivity and collective system observability.
