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Structural Controllability of Networked Relative Coupling Systems

This paper studies controllability of networked systems in which subsystems are of general high-order linear dynamics and coupled through relative variables (called networked relative coupling systems, NRCSs in abbreviation) from a structure perspective. The purpose is to search 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, which are 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 under some necessary connectivity conditions, all parameter-dependent modes of the NRCSs are generically controllable. We then give necessary and/or sufficient conditions for structural controllability depending on subsystem dynamics and the connectivity of network topologies in a decoupled form for all of the three interaction fashions. We also discuss extending our results to handle certain subsystem heterogeneities and show their direct applications in some practical systems, including the mass-spring-damper systems and the power networks.

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