Block Backstepping Control of MIMO Systems

Based on the Lyapunov stability theorem, a methodology of designing the block backstepping controller for a class of multi-input multi-output (MIMO) systems is proposed to solve the tracking problem. Some adaptive mechanisms are embedded both in the virtual input controller and in the backstepping controllers so that not only are the perturbations suppressed, but also some knowledge of the upper bound of perturbations is not required. Finally, an example of controlling a two-axis piezoelectric microposition is used to demonstrate the feasibility of the proposed methodology.