In this paper, we study the problem of closed-loop power allocation in mobile cellular-communication networks subject to multiplicative uncertainty. Multiple-access interference, nonuniform quantization, and finite wordlength representations are all characterized by multiplicative uncertainty models in the forward and feedback paths of closed-loop power allocation strategies. The quality of service (QoS) in the cellular network is evaluated with respect to signal to interference-noise ratio after the estimation process, where the uplink channel (mobile users to base station) is addressed under arbitrary round-trip delays per user. The multiplicative uncertainty terms are modeled by a stochastic framework, where 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 the sensitivity and its complementary transfer functions of the closed-loop system. The distributed power control scheme that maximizes the stability upper bounds is derived that depends on the round-trip delay per user, and whose structure enables simplifying the inequalities to evaluate robust stability. By establishing a numerical relation between the size of the interference and the multiplicative noise, a unique stability bound is derived for closed-loop power allocation. A numerical evaluation was carried out in a code-division multiple-access cellular network with multiple base stations, and under distinct QoS requirements.