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  1. We consider the problems of asymptotic stability and robustness in large-scale second-order consensus networks and vehicle platoons in the discrete-time domain. First, we develop a graph-theoretic methodology to design the state feedback law for the second-order consensus networks and vehicle platoons in a discrete-time framework. We analyze the stability of such networks based on algebraic properties of the Laplacian matrices of underlying graphs and each vehicle’s update cycle (also known as the time step). We further provide a necessary and sufficient condition of stability of a linear second-order consensus network in the discrete-time domain. Moreover, we evaluate the robustness of the consensus networks by employing the expected value of the steady-state dispersion of the state of the entire network, also known as squared H2-norm, as a performance measure. We show the connection between performance measures with respect to network size, connectivity, and the update cycle. The main contribution of this work is that we provide a formal framework to quantify the relation between scaling performance measures and restrictions of the vehicles’ update cycles. Specifically, we show that denser networks (i.e., networks with more communications/edges) require faster agents (i.e., smaller update cycles) to outperform or achieve the same level of robustness as sparse networks (i.e., networks with fewer communications/edges). 
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