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Robust control of non-linear systems with disturbances and uncertainties is addressed in this study using disturbance observer-based control (DOBC) technique. In this framework, the `disturbance` is a generalised concept, which may include external disturbances, unmodelled dynamics and system parameter perturbations. The existing DOBC methods were only applicable for the case where disturbances and uncertainties satisfy so-called matching condition, that is, they enter the system in the same channel as the control inputs. By appropriately designing a disturbance compensation gain vector in the composite control law, a non-linear disturbance observer-based robust control method is proposed in this study to attenuate the mismatched disturbances and the influence of parameter variations from system output channels. The proposed method is applied to a missile system with non-linear dynamics in the presence of various uncertainties and external disturbances. Simulation shows that, compared with the widely used non-linear dynamic inversion control (NDIC) and NDIC plus integral action methods, the proposed method provides much better disturbance attenuation ability and stronger robustness against various parameter variations.