Generic Controllability of Undirected Networks of Relative Coupling Identical Systems

In this paper, controllability of undirected networked systems (NSs) with relative coupling identical subsystems is considered, where each subsystem is of fixed general single-input-multi-output dynamics. The underlying graph of the subsystem interaction topology is vector-weighted, rather than scalar-weighted. The aim is to find conditions under which the NS is generically controllable, i.e., for almost all vector values for interaction links of the network topology, the whole system is controllable, which is also called structural controllability. Necessary and sufficient conditions are given for the considered NS to be structurally controllable. A promising point of the obtained conditions is that, they depend only on controllability and observability of each subsystem, as well as the connectivity property of the network topology. These conditions are further extended to the case where both directed and undirected interaction links exist.