Delay-dependent admissible consensualization for singular time-delayed swarm systems

Admissible consensus analysis and design problems for high-order linear time-invariant singular swarm systems with time delays are investigated. Firstly, by state decomposition, the admissible consensus problem is transformed into admissible problems of multiple singular subsystems with lower dimensions. Then, linear matrix inequality (LMI) criteria for admissible consensualization are presented, which only involve eight LMI constraints independent of the number of agents. Moreover, an explicit expression of the consensus function which is independent of time delays is presented, and the impacts of protocol states and interaction topologies on the consensus function are revealed. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.