Impulsive Quasi-Containment Control in Heterogeneous Multiplex Networks

Abstract The quasi-containment control problems of heterogeneous multiplex networks are investigated in this paper. By applying the impulsive control to the followers in the networks, and proposing the jointly directed spanning tree, all the followers converge to a convex hull which is expended by multiple leaders. Based on the Lyapunov method and comparison principle of impulsive systems, sufficient criteria are derived to guarantee that the multiplex networks can achieve quasi-containment control. It is found that the upper bound of the errors is closely related to the topology of the multiplex networks, the coupling strength, and the maximal impulsive interval. In addition, the multiplex networks with time delays are further discussed. It is shown that the followers also can achieve quasi-containment control for the multiplex networks with time delays. Finally, the effectiveness of the theoretical results is verified by a two-layers network.