Consensus analysis of multiple double-integrator agents with impulsive protocol and time-delays

Consensus problem for a group of double-integrator agents is investigated, under impulsive protocol and communication time-delays. For each agent, the relative information of position and the one of velocity are utilized for the control input. These information are both suffered communication time-delays caused by transmission on networks. We employ state transformation to build equivalent condition of consensus solving, that is protocol parameters, impulsive period, and time-delay satisfy some algebraic inequalities, and topology owns spanning tree. The consensus state where all the agents reach finally is also provided. Simulations on directed topology and undirected topology are worked out.