Distributed impulsive control for signed networks of coupled harmonic oscillators with sampled positions

This article considers the distributed impulsive control problem for a signed network composed by coupled harmonic oscillators based on relative position data, where the topology graph can be either structurally balanced or unbalanced, consisting of positive and negative links. First, an impulsive control algorithm is proposed for the network by utilizing both current and previous sampled positions. A necessary and sufficient condition is established such that the impulsive-controlled network can exhibit convergent behaviors, including bipartite synchronization, interval bipartite synchronization, and global stabilization. Second, some discussions are further provided to analyze two additional impulsive control algorithms designed with either current or previous sampled positions, in which it is shown that the former algorithm cannot lead to the convergent behaviors of the network, while the latter algorithm can solve the distributed impulsive control problem of the network under some appropriate conditions. Finally, simulation examples are given to illustrate the theoretical analysis.