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Convergence speed and distributiveness are important properties of a power-control algorithm in order to evaluate its potential for use in cellular radio systems. Most of the power-control algorithms in literature are derived from numerical linear algebra or linear control theory and, consequently, are in linear form. This paper, on the other hand, proposes a (sigmoid-basis) nonlinear power-control algorithm that is fully distributed and first order. The algorithm is obtained by discretization of the differential equation forms of the algorithm shown to be stable in the case of a feasible system. It is shown to be quadratically convergent in the neighborhood of its fixed point. We carried out computational experiments on a code-division multiple-access system. The results indicate that our algorithm significantly enhances the convergence speed of power control in an estimation error-free scenario and is more robust against estimation errors as compared with the linear distributed power-control algorithm of Foschini and Miljanic as a reference algorithm. The proposed algorithm was also verified with an advanced dynamic system simulator.