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This paper investigates stability and robustness of a gradient-type power control algorithm for multicell CDMA wireless communication networks in the presence of time-delays and disturbances. The time-delays in individual communication channels between mobiles and base stations are allowed to take place independently. The disturbances represent power noises, unmodeled secondary interference and variation of channel gains. We show that the power control system remains integral input-to-state stable with respect to the disturbances for arbitrarily large time-delays for a reasonably large class of pricing functions determining the gradient. For unbounded gradients, a stronger property called the input-to-state stability is proved. The results are based on explicit construction of Lyapunov-Krasovskii functionals for the multicell network via an iISS small-gain theorem.