Based on the Lyapunov stability theorem, a methodology of designing the block backstepping controller for a class of multi-input systems with matched and mismatched perturbations is proposed in this article. Some adaptive mechanisms are embedded both in the virtual input controller and in the backstepping controllers so that not only are the mismatched perturbations suppressed, but also part knowledge of the upper bound of perturbation is not required. Finally, an example of stabilising the control-moment-gyro devices is presented to demonstrate the feasibility of the proposed methodology.