Abstract: The notation of a guaranteed attractor disturbance rejection is presented for a class of system with persistent disturbance. Based on a back stepping design, Barbalat lemma and Lyapunov theory, and by solving a quadratic matrix inequality (QMI), an adaptive scalar robust controller is designed for a class of this kind of system to suppress its states to a bounded attractor, and the QMI is transformed into linear matrix inequality (LMI). The further criterion of the attractor’s minimization is brought forward in the form of LMI, and so further optimizes the effect of disturbance rejection control. As application, the roll motion of a fishery administration ship in the random oblique wave is discussed. Then the designed disturbance rejection controller is used as rudder moment to control its roll motion, and the effect of the guaranteed attractor roll stabilization is verified.