Resumen de The controllability Gramian of lattice graphs

Isaac Klickstein, Francesco Sorrentino

• The control of networked dynamical systems continues to receive much attention across the engineering and scientific research fields. Here, we investigate the control of lattice systems which provides analytical insight into the relationship between network structure and controllability. First we derive the exact expression for the individual elements of the controllability Gramian of infinite lattice systems. Second, we focus on nearest neighbor lattices for which the distance between nodes appears in the expression for the controllability Gramian. We show that common control energy metrics scale exponentially with respect to the maximum of all the distances between driver nodes and target nodes.