  This paper studies the controllability of networked relative coupling systems
(NRCSs), in which subsystems are of fixed high-order linear dynamics and
coupled through relative variables depending on their neighbors, from a
structural perspective. The purpose is to explore conditions for subsystem
dynamics and network topologies under which for almost all weights of the
subsystem interaction links, the corresponding numerical NRCSs are
controllable, which is called structurally controllable. Three types of
subsystem interaction fashions are considered: 1) each subsystem is
single-input-single-output (SISO), 2) each subsystem is
multiple-input-multiple-output (MIMO), and the weights for all channels between
two subsystems are identical, and 3) each subsystem is MIMO, but different
channels between two subsystems can be weighted differently. {We show that all
parameter-dependent modes of the NRCSs are generically controllable under some
necessary connectivity conditions. We then derive necessary and/or sufficient
conditions for structural controllability depending on subsystem dynamics and
network topologies' connectivity in a decoupled form for all the three
interaction fashions.} We also extend our results to handle certain subsystem
heterogeneities and demonstrate their direct applications on some practical
systems, including the mass-spring-damper system and the power network.
