This paper presents a tracking design methodology applicable to multivariable non-affine-in-control systems. The main focus is on solving the tracking problem for non-linear systems whose dynamics depend non-linearly on the control input. The latter is designed to be faster than the main system dynamics. Using singular perturbation theory along with the Lyapunov stability theorems, it is shown that the proposed controller approximates an unknown dynamic inversion based solution with bounded errors, provides closed-loop stability, and solves the tracking problem with bounded errors. Simulations illustrate the theoretical results.