## 1 Introduction  
During recent decades, the problem of ship roll stabilization has been increasingly tackled by researchers due to a demand for higher cargo safety, on-board staff effectiveness, passenger comfort, and on-board equipment operation [1; 2; 3]. In order to reduce the effect of roll motion, several solutions have been devised. Examples include bilge kels, gyroscopic stabilizers, anti-rolling tanks, active fins, and rudder roll stabilization [3]. Among these promising techniques, the fin stabilizer is one of the most interesting devices due to its reliability, engineering feasibility and high efficiency. The effectiveness of the fin stabilizer is demonstrated especially when the ship navigates at higher speeds, as it can provide considerable damping to the ship roll angle and the corresponding roll rate [4]. As a key problem in sailing, environmental disturbances, such as waves, sea winds and underwater currents, will damage the stability of the system and induce rolling. Some attempts to deal with these disturbances can be found in [3; 4; 5; 6; 7; 8]. Due to the difficulty in predicting the value of external disturbances, [PERSON] et al. [3] decoupled the fin hydrodynamic force and severe disturbances using a force sensor and a novel mechanical decoupling method. [PERSON] et al. [4] reduced the impact caused by unknown disturbances using a robust control method when the discrete fin stabilizer system model is confronted with bounded additive disturbances. In [5], a self-tuning proportion-integration-differentiation (PID) controller, based on two multilayer neural networks, was constructed for suppressing the impact of the external disturbance with self-tuning PID gains. In order to eliminate the moments induced by disturbance, in [6] a lift-feedback control of fin stabilizersbased on a new measuring lift device was proposed. In [7], the simulation of the multi-island genetic algorithm (MIGA) PID controller showed that the fin stabilizer is an effective method of roll angle reduction in the presence of external disturbances. However, the aforementioned methods will inevitably increase the controller design difficulty and the computational complexity of the control system. In addition, the disturbance observer is capable of estimating the unknown disturbance while integrated with other advanced control techniques. In [9], a nonlinear disturbance observer is proposed the multilink robotic manipulators; this observer relaxes the constraints on the prior knowledge of the acceleration signals. [PERSON] et al. [10] investigated the combination of the disturbance observer and the prescribed performance control methods, which eliminate the impact of these external disturbances effectively. In this study, the impact of the external disturbance was also suppressed through the adoption of a nonlinear disturbance observer. When performing certain tasks, the roll angle of a ship should be adjusted through an expected dynamic process and the steady-state working performance. The controllers that are capable of providing this desired dynamic process and steady-state performance are usually based on the prescribed performance control [11; 12; 13; 14; 15; 16]. In [11], a robust controller for a multi-input multi-output (MIMO) system was proposed based on adaptive control with respect to the prescribed performance. [PERSON] et al. [12] proposed an adaptive prescribed performance controller where the error convergence trajectory, the overshoot, and the steady-state error are constrained by a prescribed performance function. The corresponding studies also investigated some actual systems, such as flexible air-breathing hypersonic vehicles [13], variable stiffness actuated robots [14], and unknown high-order nonlinear multi-agent systems [16]. Considering the superior characteristics of the prescribed performance control, it may be one of the most effective strategies to provide an expected performance for the ship rolling system.