Measures of Modal Controllability for Network Dynamical Systems

The quantification of controllability has gained renewed interest in the context of large, complex network dynamical systems. In some application areas such as com-putational neuroscience, there is a large interest in modal controllability, which describes the ability of an input to control the modes of a system. In case of a linear system, the modes of the system are given by the left eigenvectors associated with the system matrix. In this work, we identify mode specific and gross metrics for modal controllability for both discrete and continuous systems. Our metrics are based on energy requirements to move along a given mode and find applications in problems involving selection of driver nodes for minimizing control effort along particular modes of the network. We illustrate the use of these metrics on real world networks.