Design of block backstepping controllers for a class of perturbed multiple inputs and state-delayed systems in semi-strict-feedback form

Based on the Lyapunov stability theorem, an adaptive block backstepping control scheme is proposed in this paper for a class of multi-input systems with mismatched multiple state-delayed perturbations to solve regulation problems. The traditional backstepping control method is modified so that it can be directly applied to systems in block semi-strict-feedback form. The terms in the dynamic equations which do not satisfy the block strict-feedback form are accumulated in the last design step and are suppressed effectively by the adaptive gains, so that the property of asymptotic stability is achieved. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, hence the least upper bounds of perturbations are not required to be known in advance. A numerical example and a practical application are also given for demonstrating the feasibility of the proposed control scheme.