AbstractIn this paper we develop a discrete‐time adaptive stabilization algorithm based on a one‐step backward‐horizon cost criterion. By optimizing the cost with respect to the update step size, we obtain a gain update law that guarantees convergence of the plant states. The convergence proof is based on a modified Lyapunov technique. We extend the algorithm to include integral control for rejecting constant disturbances and we present an experimental application to DC motor positioning system. Copyright © 2003 John Wiley & Sons, Ltd.