Adaptive Synchronization in Lipschitz-Type Multilayer Heterogeneous Networks Subject a Leader

This paper considers the Lipschitz-Type multilayer heterogeneous networks subject a leader. The dynamics of the nodes and the connections between the layers of the network are heterogeneous, and the leader has dynamical inputs. A class of adaptive coupling gains is proposed in this paper. By utilizing Lyapunov stability theory and matrix theory, the synchronization criteria of the heterogeneous multilayer networks is derived, and the error system will converge to a bounded set. Finally, the correctness of the synchronization criteria is verified by a numerical example.