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In this paper we consider the $\mathcal{H}_2$-norm of networked systems withmulti-time scale consensus dynamics. We develop a general framework for suchsystems that allows for edge weighting, independent agent-based time scales, aswell as measurement and process noise. From this general system description, wehighlight an interesting case where the influences of the weighting and scalingcan be separated in the design problem. We then consider the design of the timescale parameters for minimizing the $\mathcal{H}_2$-norm for the purpose ofnetwork resilience.

Time scale design for network resilience