H∞ synchronization of a class of complex networks

This paper deals with H∞ synchronization problem for a class of complex networks with each node being a general Lur´e system with infinite equilibria. On the basis of the Lyapunov theory, linear matrix inequality (LMI) conditions guaranteeing the global asymptotic synchronization of all nodes with desired H∞ performance are established. In addition, the following interesting result is derived: the synchronization problem for the whole Nn-dimensional dynamic networks can be converted into the simple n-dimensional space in terms of only two LMIs. Finally, a concrete application to mutually coupled phase-locked loop networks shows the validity of the proposed approaches.