Output consensus for high-order linear time-invariant swarm systems

Output consensus analysis and design problems of high-order linear time-invariant swarm systems are investigated. First, an output consensus subspace and a complement output consensus subspace are introduced. By output projection onto the two subspaces and the partial stability theory, a necessary and sufficient condition for output consensus is presented, and an explicit expression of the output consensus function, which is jointly determined by the interaction topology and initial states of all agents, is given. Especially, it is shown that the output consensus function is completely determined by initial states of all agents if the interaction topology is balanced. Then, an approach to determine gain matrices in consensus protocols of swarm systems is proposed, which has less calculation complexity. Finally, a numerical example is shown to demonstrate theoretical results.