Admissible L2L2 consensus for singular time-delayed swarm systems with external disturbances

• Admissible L2L2 consensus problems for singular swarm systems are proposed.
• The impacts of time delays and external disturbances on singular swarm systems are investigated.
• The L2L2 evaluation approach has fewer limitations on the structures of consensus functions.

Admissible consensus analysis and design problems for high-order linear time-invariant singular swarm systems with time delays and external disturbances are investigated. Firstly, by the state space decomposition, a necessary and sufficient condition for admissible consensus is given and an approach is presented to determine consensus functions on the basis of different impacts of initial states of agents and external disturbances, which describe the absolute motions of singular swarm systems as a whole. Then, an L2L2 evaluation approach which requires fewer limitations on the structures of consensus functions is proposed to determine the influences of external disturbances on relative motions among agents, and linear matrix inequality criteria for admissible L2L2 consensus and consensualization are shown. Finally, numerical simulations are presented to demonstrate theoretical results.