Consensus in second-order multi-agent systems via impulsive control using position-only information with heterogeneous delays

This study investigates the consensus problem of second-order multi-agent systems (MASs) via impulsive control using position-only information with communication delays. The communication delays between any two distinct agents are different which can be larger than one impulsive period. A distributed impulsive consensus protocol is designed, in which only the delayed sampled relative positions to neighbours and the relative position to the last sampling state are utilised. By introducing some virtual subgraphs and performing three steps of model transformation, the consensus problem of original continuous-time system is converted to the stability problem of a discrete-time expanded error system. Some necessary and sufficient criteria are derived to grantee the dynamic average-consensus of the MAS. Furthermore, a special case, that is, the delays less than one impulsive period, is discussed, and the bounds of impulsive periods for the dynamic average-consensus are obtained in explicit expressions for both the undirected and directed communication graphs, respectively. Two numerical simulation examples are given to illustrate the effectiveness of theoretical results.