Theoretical problems on self-tuning control include stability, performance and convergence of the recursive algorithm involved. In this paper, the problem of controlling minimum or non-minimum phase auto-regressive models with constant but unknown parameters is considered. The stability of an algorithm obtained by combining a recursive estimator for the controller parameters and a generalized minimum variance criterion is proved. The main result is the theorem which assures the overall stability for the closed-loop system in presence of white noise in the input-output relation, where the estimated parameters do not necessarily converge to the true values. The algorithm is proved by the Lyapunov theory. (C) 2008 Elsevier Ltd. All rights reserved.