Abstract: This paper presents an adaptive robust control scheme for a discrete-time plant subject to both coprime factor perturbations and unknown external disturbances. Firstly, we establish nice continuity properties for l1 optimization resulting from optimal robust control of discrete time uncertain systems with coprime factor perturbations. Then, we propose a robust parameter estimate algorithm with variant dead zone. Finally, combining the proposed parameter estimate algorithm with optimal l1 robust control, we present a novel adaptive robust control scheme for plants with coprime factor perturbations based on the certainty equivalence principle. With the continuity properties of l1 optimization established in this paper, the proposed adaptive scheme is shown to be uniformly stable. A posterior computable condition for the stability of the adaptive scheme is also provided in this paper.