Multiple Time-Scales in Network-of-Networks

Abstract

This paper examines a multiple time-scale system where each layer of time-scale dynamics corresponds to a network. Coupling between layers induces a network-of-networks dynamic system. Assuming a hierarchical interaction structure between network time-scale layers with sufficient time-scale differences, layers can be studied under a separation principle. We describe stability of the network-of-networks through a composite Lyapunov function and provide a bilinear matrix inequality condition to guarantee asymptotic stability. Techniques are proposed to adapt this inequality into a linear matrix inequality condition making it computationally efficient to solve as a convex optimization problem. ..