A robust servo problem with an H-infinity norm constraint is investigated based on the LMI (Linear Matrix Inequality) approach to the H-infinity, control problem. The following results are obtained. (1) A necessary and sufficient condition for the existence of an H-infinity controller with robust tracking property is derived. It consists of the following two independent conditions : (i) the existence of an H-infinity controller; (ii) a boundary constraint at the reference mode. (2) If there exists an H-infinity controller with robust tracking performance, there exists one whose order equals the sum of an H-infinity controller and the internal model.