In this paper, the problem of power allocation in a wireless network is studied with a distributed perspective by taking into account multiple-access interference in the communication channel, non-uniform quantization and floating-point operations. These three effects can be characterized by multiplicative uncertainty models in the forward and feedback paths of a closed-loop power control strategy. The quality of service (QoS) in the wireless data transmission is evaluated with respect to signal to interference-noise ratio (SINR) after the estimation process, where the uplink channel (active users to base station) is addressed by its implications with respect to battery consumption. The multiplicative uncertainty terms are modeled by a stochastic framework, and the mean-square small gain theorem is employed to evaluate robust stability. Two inequalities are then derived to check internal stability with respect to the norms of the multiplicative uncertainty terms, and sensitivity and complementary sensitivity transfer functions of the closed-loop system. As a case study we considered an LQG controller in each active user for power allocation, whose structure allows to derive simplified inequalities to evaluate robust stability.