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Robust synchronization of complex networks with uncertain couplings and incomplete information

The mean square exponential (MSE) synchronization problem is investigated in this paper for complex networks with simultaneous presence of uncertain couplings and incomplete information, which comprise both the randomly occurring delay and the randomly occurring non-linearities. The network considered is uncertain with time-varying stochastic couplings. The randomly occurring delay and non-linearities are modelled by two Bernoulli-distributed white sequences with known probabilities to better describe realistic complex networks. By utilizing the coordinate transformation, the addressed complex network can be exponentially synchronized in the mean square if the MSE stability of a transformed subsystem can be assured. The stability problem is studied firstly for the transformed subsystem based on the Lyapunov functional method. Then, an easy-to-verify sufficient criterion is established by further decomposing the transformed system, which embodies the joint impacts of the single-node dynamics, the network topology and the statistical quantities of the uncertainties on the synchronization of the complex network. Numerical examples are exploited to illustrate the effectiveness of the proposed methods.