On the impact of edge modifications for networked control systems

Abstract

Abstract This paper investigates the impact of addition/removal of edges in complex networks. Growing a network by the addition of edges has for instance been suggested as a way to improve network robustness to external disturbances. Moreover, when network controllability is considered, designing edge additions is a promising alternative to add more actuation capabilities in order to improve different performance metrics. We quantify the impact of an edge modification with the H∞ and H2 norms. For networks with positive edge weights we show how the H∞ norm can be computed exactly for each possible single edge modification, while for the H2 norm we instead obtain a lower bound. This bound is linked to the trace of the controllability Gramian, hence it can be used for instance to reduce the energy needed for control.