Outer synchronization of uncertain general complex delayed networks with adaptive coupling

In this paper, the outer synchronization of uncertain complex delayed networks with adaptive coupling is studied. Under some assumptions, a simple adaptive controller, the update laws for the weight strengths of the coupling configuration matrix and the update laws for system parameters of node dynamics are obtained to realize the outer synchronization based on Barbalat's Lemma. By means of the presented controllers and corresponding update laws, the outer synchronization between two complex delayed networks with adaptive coupling can be achieved without calculating the eigenvalues of the coupling configuration matrix. Simultaneously, the outer coupling matrix of the network and the system parameters of node dynamics are also identified. Furthermore, the proposed method can be easily extended to obtain consensus in the multi-agent systems. Some illustrative examples are finally provided to verify the effectiveness of the proposed scheme.