This paper addresses the control of a class of nonlinear, multivariable, high-index differential-algebraic-equation systems with external disturbances. Initially, an algorithmic procedure is developed to derive an equivalent state-space realization of the constrained system, valid for arbitrary disturbances. Then, on the basis of the derived state-space realization, a feedforward/feedback controller is developed to completely eliminate the effects of the measurable disturbances and induce a well-characterized input/output behavior in the constrained system. The application of the proposed control methodology is illustrated on a high-purity absorption column.