Quasi‐synchronization of multilayer heterogeneous networks with a dynamic leader

Abstract

SummaryThis article considers the pinning quasi‐synchronization problem for a class of leader‐following multilayer heterogeneous complex networks. The leader has nonzero control inputs that are unavailable to the followers. Multilayer heterogeneous networks with heterogeneous node dynamics and two different layer structures are proposed in this article. Two types of discontinuous coupling laws are designed for achieving synchronization in multilayer heterogeneous networks. Based on Lyapunov stability theory and the matrix theory, some sufficient criteria for pinning quasi‐synchronization are derived, and the upper bound of quasi‐synchronization errors is solved. Finally, numerical simulations are performed to illustrate the effectiveness of the theoretical results.