The steady states of tracking systems incorporating self-selecting controllers and linear multivariable plants exhibit limit tracking when none of the plant outputs exceeds its corresponding set point (i.e. its limit value) and the number of pairs of equal plant outputs and set points is not less than the rank of the plant steady-state transfer-function matrix. The condition for the feasibility of limit tracking is given. An approach to the synthesis of limit-tracking systems is proposed that utilizes an order-reduction technique to reduce the number of separate set-point tracking controllers frompCmtop− m + 1 in the case ofm-input/p-output plants while guaranteeing the existence of the steady states of such tracking systems.