Synchronization of delayed multi-agent systems over uncertain networks

This paper is concerned with the mean square exponential (MSE) synchronization problem for the multi-agent systems with time delays over uncertain networks, where the uncertainty lies in that the links between subsystems are varying stochastically according to certain rules. Firstly, applying the theories of coordinate transformation, Kronecker product and Laplacian matrix, the synchronization problem for the addressed multi-agent systems is transformed into investigating the exponential stability in the mean square for a modified system. Then, by constructing an appropriate Lyapunov functional, sufficient criteria are derived which assure the MSE stability of the transformed system, and hence guarantee the MSE synchronization of the original multi-agent systems. Moveover, through decomposing the transformed system, an easy-to-check sufficient condition is given which is based on the relationships between the system parameters of the single agent, the network topology and the statistical characterizations of the network uncertainties. Simulation examples are presented in the end of the paper to demonstrate the validity of the obtained results.