Regularity and minimum-phase properties in nonlinear asymptotic tracking loops

If an analytic nonlinear plant is (1) dynamically input-output decouplable in neighborhood of the origin and (2) minimum-phase, it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in C_mⁿ[0, ∞), the space of N-times continuously differentiable functions taking values in R^m. It is established in the present work that, for locally controllable MIMO (multiple-input multiple-output) systems, under certain technical assumptions related to system inverses and zero dynamics, conditions (1) and (2) are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories. Necessary conditions for input-output decouplability in a neighborhood of a given point are also discussed