Determination of configuration matrix element and outer synchronization among networks with different topologies

In this paper, we research the outer synchronization among discrete networks with different topologies. Based on Lyapunov theorem, a novel synchronization technique is designed. Further, the control inputs of the networks and the adaptive laws of configuration matrix element are obtained. In the end, a numerical example is given to illustrate the effectiveness of the synchronization technique. It is found that the designed control input of the networks ensures the convergence of the errors among the networks to zero. And the designed adaptive law of configuration matrix element can replace effectively configuration matrix element in networks.