Stability study is essential in the control design of optimal quasi‐stationary tracking systems with parameter variations. In this paper, the asymptotic stability conditions of such systems given in the author's previous results [8, 13, 14] are developed. The conditions based on the design methods of traditional technique and model‐following technique can guarantee the closed‐loop system to be stable at the norminal conditions only. However, based on the guaranteed cost design technique, the closed‐loop system with allowable parameter variations is asymptotically stable because the guaranteed cost can be made to be a Lyapunov function for the closed‐loop system.