Exploring the Impact of Memory on Network Controllability

In this paper, we examine how adding memory to nodes of a network system impacts its controllability properties. Specifically, we analyze the behavior of the control energy of a continuous-time linear network system and that of its lifted version, obtained by allowing each node to have nontrivial internal dynamics. We discuss how to compare the effect of a control input on the original and lifted network, and show that, for line networks, adding memory may reduce the worst-case control energy by a factor that is exponential in the network size.