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This paper provides a detailed analysis and performance treatment of a class of discretetime systems with an eigen-spectrum gap coupled over networks. We deploy tools from time-scale modeling (TSM) theory to develop rigorous reduced-order models to aid in the stability analysis of these multiple time-scale networked systems over fixed and undirected graph topology. We establish that the controller gain matrices can be determined by solving convex optimization problems in terms of finite lineardoi:10.33401/fujma.815819 fatcat:cx6ois2slrfihbdk7oc4p4lyga