Consensus problems for high-order linear time-invariant swarm systems

Consensus problems for high-order continuous-time linear time-invariant swarm systems with directed interaction topologies are investigated. A new method to deal with consensus problems is proposed based on state space decomposition. Two subspaces of a complex space are introduced, namely a consensus subspace and a complement consensus subspace. Based on this decomposition, necessary and sufficient conditions for consensus and consensualizability are presented respectively. An approach for determining and designing the consensus function which may be time-varying is shown. The applications of theoretical results in multi-agent supporting systems are studied.