Structural controllability of networked relative coupling systems

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.