Controllability of Heterogeneous Networked Systems With Nonidentical Inner-Coupling Matrices

This article investigates state controllability of high-dimensional linear networked systems with weighted topology, heterogeneous node dynamics, and nonidentical inner-coupling matrices. The focus is on how the node heterogeneity and nonidentical inner-coupling may affect the controllability of the system. It is found that the heterogeneous networked systems with nonidentical inner-coupling are controllable, even if the identically inner-coupled counterparts are uncontrollable, and vice versa. The finding also reveals the influence of the heterogeneity of the inner-coupling matrix on the network controllability. Some necessary and sufficient conditions for general linear systems with nonidentical inner-coupling, including some special cases to retain controllability, are derived. For typical structure networks, the controllability conditions depend solely on the specific form of the coupling matrix between a small number of nodes, but are independent of the coupling relationship between the remaining nodes. Some examples are given for illustration and verification.