Time-Scale Separation in Networks: State-Dependent Graphs and Consensus Tracking

This paper studies the coupled dynamics spanning multiple time-scales that arise in networked systems. Two particular cases are examined. In the first case, agents evolve according to the consensus dynamics over state-dependent graphs whose weight dynamics are slow varying. In the second, the consensus dynamics are coupled to rapidly evolving nonlinear node dynamics. In both instances, graph-based guarantees are provided that certify the existence of a separation principle across time scales. Further, the effect of the network's structure on the composite multiple time-scale system's stability and basin of attraction is quantified in each case. As illustrated by specific numeric examples, these results provide designers with a network-centric approach to improve the performance and stability of such coupled systems.