Time scale design for network resilience

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.