A decomposition approach to output tracking for multivariable nonlinear non-minimum phase systems

It is common wisdom that if a multivariable nonlinear system, affine in the controls, is non-minimum phase then dynamic inversion is not applicable for output tracking. We introduce a new approach in which a multivariable nonlinear control system is decomposed into two parts: a minimum phase part and a non-minimum phase part. For the minimum phase part dynamic inversion can be used to achieve output tracking. The non-minimum phase part can be suitably controlled by linear feedback, but the decomposition often leads to a simpler non-minimum phase problem than the original. It is necessary to restrict the class of output commands to be tracked according to the properties of the non-minimum phase part. These restrictions are identified by using results from robust control theory for commands that are perturbations of a command corresponding to a closed loop equilibrium.