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