Pinning-Controllability Analysis of Complex Networks: An M-Matrix Approach

This paper presents a systematic framework to analyze the global pinning-controllability of general complex networks with or without time-delay based on the properties of M-matrices and directed spanning trees. Some stability criteria are established to guarantee that a network can be globally asymptotically pinned to a homogenous state. By partitioning the interaction diagraph into a minimum number of components, a selective pinning scheme for a complex network with arbitrary topology is proposed to determine the number and the locations of the pinned nodes. In particular, this paper deeply investigates the roles of network nodes in the pinning control, including what kind of nodes should be pinned and what kind of nodes may be left unpinned. Numerical simulations are given to verify the theoretical analysis.