Impulsive consensus for second-order multi-agent systems with a reference velocity and input delays

In this brief, a distributed impulsive algorithm for second-order multi-agent systems with a group reference velocity and input time delays is proposed. A distinctive feature of the algorithm is to address second-order consensus problems with local instantaneous interaction, where each agent can only exchange the information with its neighbors at a series of discrete-time instants and follow a desired reference velocity in the meantime. Some generic criteria for such algorithm over, respectively, directed fixed and switching network topologies are derived analytically. It is shown that consensus can be asymptotically reached if the interaction graph of the system has a spanning tree and the input time delays are less than the interaction intervals, which is assumed to be less than a given threshold value. Subsequently, numerical simulations are given to illustrate and visualize the effectiveness and feasibility of the theoretical results.