Scalable Stability and Time-Scale Separation of Networked, Cascaded Systems

In this paper, we investigate the effect of insufficient time-scale separation between inner and the outer loops in networked, cascaded systems. First, a qualitative model is developed where the stability of a cascaded system is analyzed in terms of the gains acting at the outer and inner loops. Next, interconnected cascaded systems are considered, which represent networks congested by data sent by multiple clients. Then, the effect of the number of clients for the performance is examined through the scalable stability notion, which guarantees positively lower-bounded convergence rates with respect to the number of clients.