Sufficient conditions for robust stability of multivariable quadratic dynamic matrix controllers with an end condition (EQDMC) are developed, and the effect of these conditions on closed-loop performance is examined. Hard and soft constraints on process inputs and outputs, and process modeling uncertainty are present. Modeling uncertainty is quantified in the time domain as upper and lower bounds on the coefficients of a finite pulse; response process model. The robust stability conditions that we develop involve the prediction and control horizon lengths and a set of inequalities that the move-suppression coefficients in the on-line EQDMC objective function must satisfy. These conditions imply that for processes with modeling uncertainty, the move-suppression coefficients could be quite large and quite sensitive to the control horizon length and process modeling errors. This could make the EQDMC controller conservative, thus significantly deteriorating performance. To determine the optimal control horizon length corresponding to the best robust performance of the EQDMC controller for a class of disturbances, follow the proposed EQDMC controller design methodology. To illustrate this methodology simulations on an SISO example and a 2 x 2 subsystem of the Shell Standard Control Problem are presented.