Backstepping control of multi-input non-linear systems

A methodology of designing the block backstepping controller for a class of multi-input non-linear perturbed systems is proposed to solve the regulation problem in accordance with the Lyapunov stability theorem. The designed constant gains, which are embedded in the virtual input controllers, can effectively overcome more general mismatched perturbations than some works can. Furthermore, the asymptotical stability can be achieved by the proposed controller. Finally, an example of controlling the control-moment-gyro devices is used to demonstrate the feasibility of the proposed methodology.