In wireless networks under interference, power control is of the utmost importance to guarantee Quality of Service during data transmissions. A distributed perspective is commonly preferred to design controllers in each mobile user in the network for power allocation. The round-trip delay is a characteristic feature of wireless networks, and it was considered a known quantity in previous works. In this paper, we do not follow this assumption and propose the design of the power controller only with the information of upper and lower bounds on the round-trip delay as functions of a frequency gain. In a second stage, we relate the proposed robust design to common performance indicators, such as the step response overshoot. The proposed design rules can be applied to design a suitable robust controller for power control in a wireless network subject to interference.