Impulsive control for the synchronization of stochastic dynamical networks

Synchronization in dynamical networks is normally realized via the information exchanging along the interconnections of the nodes, and it makes the final synchronous state difficult to predict. This paper is devoted to studying the stabilization problem for complex dynamical networks in the presence of Brownian motion noise. Pinning state feedback controllers have been proved to be effective for the stabilization of complex dynamical networks with state-coupling. In this paper, we show that pinning impulsive controllers are also effective for the stabilization of dynamical networks with state-coupling, although state-coupling and impulsive controllers belong to different kinds of controllers. An algorithm is presented to select the nodes which should be controlled at each impulsive constants. The constraints on the lower and upper bounds of the impulsive interval are removed, which makes the results much less conservative. Numerical simulations are also given to demonstrate the theoretical results.