Consensus analysis and design for high-order linear swarm systems with time-varying delays

Consensus analysis and design problems for high-order linear time-invariant swarm systems with time-varying delays are dealt with. First, 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 time-delayed subsystems with low dimensions, and a method to analyze and design the consensus function is given. Then, sufficient conditions for consensus and consensualization are presented, which include only four linear matrix inequality constraints. Finally, theoretical results are applied to deal with cooperative control problems of multi-agent supporting systems.