The paper addresses the effect of interactions on the performance of decentralized control systems. Most existing tools for analyzing the effect of interactions assume perfect control up to the system bandwidth, and furthermore neglect the phase contributions from subsystem interactions. Here we show that for most systems, and in particular large scale systems, the assumption of perfect control is a poor one. Furthermore, we show that the phase contributions of the interactions can be crucial both for stability and performance. Based on this we develop a new tool, based on finite bandwidth control, for measuring interactions in decentralized control systems. We demonstrate how this tool may be used to select configurations that provide the best performance under independent tuning of the subsystems.