The two dimensional vibration control problem of a flexible marine riser with internal fluid dynamics and the ocean current is considered. The dynamic behavior of the flexible riser is described by two partial differential equations and six ordinary differential equations. To improve the vibration control performance and avoid the control spillover

the Lyapunov's direct method and high-gain observer technique are adopted to develop two output feedback boundary controllers for vibration suppression of the riser system based on its original infinite-dimensional model. With the proposed control

uniform ultimate boundedness under ocean current disturbance and uniform boundedness of the closed-loop state are proved. The simulation results have verified the effectiveness of the designed boundary control scheme.