Block backstepping controllers design for a class of perturbed non-linear systems with m blocks

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping controller is proposed in this study for a class of multi-input systems with mismatched perturbations to solve regulation problems. According to the number of blocks (m) in the plant to be controlled, m-1 virtual input controllers are firstly designed from the first block to the (m-1)th block. Then the proposed robust controller is designed in accordance with the last block. Adaptive mechanisms are used in each of the virtual input controllers as well as the robust controller, so that the least upper bound of perturbations except that of the input channel is not required during the design process. Furthermore, asymptotic stability is guaranteed by the proposed control method. A numerical example is also given for demonstrating the feasibility of the proposed control scheme.