There have been significant research efforts toward clarifying the stability of power control algorithms in wireless networks, but prior work on this topic has a key limitation, i.e., the finite-capacity nature of realistic feedback channels has not been taken considered. Under such a background, this technical note analyzes the stability of a general class of power control algorithms with single-step feedback, which implies that the feedback channel can only convey a single-step command by just using 1 bit at each time step. We first construct the system model that is generalized from a widely used power control scheme in many practical cellular networks. This system model can specify the power update behavior for a class of power control algorithms that satisfy certain properties by formulating a generalized interference function from the interference terms of these power control algorithms. We then develop an analytical framework, which shows that the considered system is uniformly asymptotically stable if proper conditions are satisfied. This framework is able to tackle the interference function with time-varying delay. Moreover, we propose parametric adaptive procedures of power control, which can adjust their parameters on demand.