Admissible consensus for descriptor multi-agent systems with switching topologies

Admissible consensus problems for high-order linear time-invariant descriptor multi-agent systems with switching topologies are dealt with. Firstly, by the state projection on the consensus subspace and the complement consensus subspace, admissible consensus problems are converted into admissible problems of a reduced-order switching subsystem, and an explicit expression of the consensus function is presented based on the First Equivalent Form. Secondly, a necessary and sufficient condition for admissible consensualization is proposed, which can guarantee the scalability of descriptor multi-agent systems since it is independent of the number of agents. Finally, numerical simulations are presented to illustrate theoretical results.