  Consensusability of multi-agent systems (MASs) certifies the existence of a
distributed controller capable of driving the states of each subsystem to a
consensus value. We study the consensusability of linear interconnected MASs
(LIMASs) where, as in several real-world applications, subsystems are
physically coupled. We show that consensusability is related to the
simultaneous stabilizability of multiple LTI systems, and present a novel
sufficient condition in form of a linear program for verifying this property.
We also derive several necessary and sufficient consensusability conditions for
LIMASs in terms of parameters of the subsystem matrices and the eigenvalues of
the physical and communication graph Laplacians. The results show that weak
physical couplings among subsystems and densely-connected physical and
communication graphs are favorable for consensusability. Finally, we validate
our results through simulations of networks of supercapacitors and DC
microgrids.
