Output consensus analysis and design for high-order linear swarm systems: Partial stability method

Output consensus analysis and design problems for high-order linear time-invariant swarm systems with directed interaction topologies are investigated. Firstly, as foundations of our approaches, several conclusions about partial stability are given. Then, two subspaces of the output space of swarm systems, namely an output consensus subspace and a complement output consensus subspace, are introduced. Based on output projection onto the two subspaces and partial stability, necessary and/or sufficient conditions for output consensus and limited-control-energy consensus are proposed respectively, an explicit expression of the output consensus function is presented based on the different contributions of initial states of agents and protocols, and an approach independent of the number of agents is shown to determine the gain matrices of output consensus protocols. Finally, a numerical example is given to demonstrate the theoretical results.