This paper extends the non-linear tracking methodology of Lin et al. to high-order and multivariable linear systems. The results provide a method of synthesizing controllers which asymptotically track a constant set-point. As with the original scheme, allowances for control limits are handled directly in the design phase, and no a posteriori compensation is required. The resulting control law consists of both linear and non-linear parts; the non-linear term being added with a view to improving the response of the system, without reducing the size of its basin of attraction. The proposed technique is demonstrated on two aerospace examples which indicate promising results.