Distributed impulsive consensus for second-order multi-agent systems with input delays

In this study, a distributed consensus protocol is proposed for second-order multi-agent systems having input time delays. A distinctive feature of the algorithm is to address consensus problems for second-order multi-agent systems with local instantaneous interaction, where each agent can only exchange the position information with its neighbours at a series of discrete-time instants and update its velocity state in the form of abrupt jumps setting. The authors also establish the consensus conditions over fixed and switching network topologies, respectively. It is shown that consensus can be exponentially reached if the interaction graph of the system is connected and the interaction intervals are less than a given threshold value. Subsequently, numerical simulations are given to illustrate and visualise the effectiveness and feasibility of the theoretical results.