Consensus problems of high-order linear time-invariant swarm systems with time delays

Consensus problems for high-order linear time-invariant swarm systems with time delays are investigated. A consensus subspace and a complement consensus subspace are introduced. By the state projection onto the two subspaces, consensus problems are converted into simultaneous stabilization problems of multiple subsystems, and an explicit expression of the consensus function is shown. In terms of linear matrix inequality, sufficient conditions for consensus and consensualization are presented, which are independent of the number of agents. Theoretical results are applied to deal with distributed control problems of Multi-Agent Supporting Systems.