Abstract
This paper provides a detailed analysis and performance treatment of a class of discrete-time 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 linear matrix inequalities with prescribed $\mathbb{H}_\infty$ and $\mathbb{H}_2$ performance criteria. As demonstrated by simulation studies, the ensuing results provide designers with a network-centric approach to improve the performance and stability of such coupled systems.
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