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This paper studies the synchronization of stochastic linear systems which aresubject to a general class of noises, in the sense that the noises are boundedin covariance but might be correlated with the states of agents and among eachother. We propose an event-based control protocol for achieving thesynchronization among agents in the mean square sense and theoretically analyzethe performance of it by using a stochastic Lyapunov function, where thestability of $c$-martingales is particularly developed to handle the challengesbrought by the general model of noises and the event-triggering mechanism. Theproposed event-based synchronization algorithm is then applied to solve theproblem of distributed estimation in sensor network. Specifically, bylosslessly decomposing the optimal Kalman filter, it is shown that the problemof distributed estimation can be resolved by using the algorithms designed forachieving the synchronization of stochastic linear systems. As such, anevent-based distributed estimation algorithm is developed, where each sensorperforms local filtering solely using its own measurement, together with theproposed event-based synchronization algorithm to fuse the local estimates ofneighboring nodes. With the reduced communication frequency, the designedestimator is proved to be stable under the minimal requirements of networkconnectivity and collective system observability.

Event-Based Control for Synchronization of Stochastic Linear Systems with Application to Distributed Estimation