Consensus problems for high-order LTI swarm systems

Consensus problems for high-order continuous-time LTI swarm systems with directed communication topologies are investigated. A new method to deal with consensus problems is proposed based on state space decomposition. Two subspaces of the state space of a swarm system are introduced, namely a consensus subspace (CS) and a complement consensus subspace (CCS). A necessary and sufficient condition for the system to achieve consensus is presented based on this decomposition. The structure of the consensus function which may be time-varying is investigated. A numerical example is shown to demonstrate theoretical results.