Does the Time-Constant of the Reference Trajectory in Predictive Control Affect the Closed-Loop Stability?

There are many ways to define the reference trajectory in predictive control. Among these, we distinguish the reference trajectory that affects the response to disturbances, and thus affects the feedback loop. Such a reference trajectory could be, for instance, the one that starts at the current output y(k) and specifies the ideal trajectory that the plant should follow in order to return to the set-point trajectory, for example, after a disturbance occurs. One possible way of generating such a reference trajectory is to assume that the reference trajectory approaches the set-point (taken as constant in this paper) exponentially from the current output value y(k), with a time-constant denoted by T_ref, defining the speed of response. The aim of this paper is to determine whether T_ref affects the closed-loop stability or not. We note that the aim of this paper as well as the approach followed is both original and the paper ends with the conclusion that redoes indeed affect the closed-loop stability