This paper develops a trajectory tracking control design algorithm to be applied in unmanned aerial vehicles (UAVs). The strategy is simple but effective and it is based on linear algebra theory. The proposed approach reforms the column space of a system of linear equations at each sampling time to ensure the tracking objective when environmental disturbances appear. This new formulation ensures a uniform signal without affecting the error convergence to zero (demonstration available), which is one of the main contributions of this work. A statistical method is used to tune the system control minimizing a pre-defined cost function. In addition, the convergence to zero of the tracking errors is demonstrated in this work. Finally, the controller’s effectiveness is tested through several simulations in realistic test scenarios in the presence of disturbances. •The trajectory tracking control in UAV under uncertainties is addressed.•The controller design for trajectory tracking is based on linear algebra.•The approach is applied in a nonlinear system with additive uncertainty.•The zero convergence of tracking error under polynomial uncertainties is demonstrated.•Several simulations in realistic scenarios were performed.