In a wireless communication network, different users share a common resource. An objective of radio resource management is to assign the resources in an effective way among the users. Power control is an important component in this setting that has been extensively studied over the last two decades. In many real networks, there are inherent time delays due to filtering of signals and control signalling. Time delays can affect stability and convergence properties of the power control algorithms. We therefore consider power control laws of higher order to include models with delays and delay compensation. The main contribution of this paper is to exploit more structure of the interference feedback to prove less conservative conditions for system stability. Our primary tool to reduce conservativeness is to use scalings in an input-output framework for stability analysis.