Robust L2 consensus of high-order swarm systems with time-varying delays

Consensus problems for high-order continuous-time swarm systems in directed networks with time delays, uncertainties and external disturbances are investigated. Firstly, the state space of a swarm system is decomposed into a consensus subspace (CS) and a complement consensus space (CCS). A necessary and sufficient condition for the system with time delays and uncertainties to achieve consensus is presented based on the state projection on CCS, and an explicit expression of the consensus function is shown on the basis of the state projection on CS. Then, a sufficient condition for the system to achieve consensus with a desired L2 performance is given. Finally, numerical simulations are shown to demonstrate theoretical results.