Input addition for the controllability of graph-based systems

In this paper, we consider dynamical graph-based systems, which are well fitted for the structural analysis of complex systems. A significant amount of work has been devoted to the controllability of such graph-based systems with application to multi-agent systems or complex networks. We give a refined analysis of the controllability through control input addition in this framework. We provide with information on the possible location of additional inputs and give tight bounds on the number of inputs to be added for controllability. These results can be easily applied to complex systems.