Abstract
This paper studies the controllability of descriptor multi-agent systems(DMASs)with signed networks,where the networks are signed,and agents have descriptor linear dynamics.First,the basis for the eigenspace of the system matrix is derived completely and qualitatively by leveraging the maximum general-ized left Jordan chain defined in this paper.Taking advantage of the explicit form of the basis,necessary and sufficient conditions for the controllability of DMASs are established.Furthermore,a necessary and sufficient condition is provided to ensure the controllability of DMASs with heterogeneous dynamics.Particularly,for some special cases,controllability conditions are expressed more precisely in terms of eigenvectors.Then,the relationship between the controllability of DMASs with signed and unsigned networks is investigated.It is shown that the controllability of DMASs under structurally balanced signed networks is equivalent to that under the associated underlying unsigned networks whether the individual dynamics is homogeneous or heterogeneous.Finally,theoretical results are applied to the multi-agent supporting systems.
维普
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