Vibration control for a flexible satellite system with output constraints

In this paper, a flexible satellite system is described by two governing equations and eight boundary conditions through Hamilton’s principle. Based on Lyapunov’s direct method, a barrier Lyapunov function is employed to design two boundary control laws and analyze the stability of the closed-loop system. By employing the proposed control schemes, the vibrations of the flexible satellite are suppressed to zero, the angle displacement converges to the desired angle, and both the tracking error and the elastic deflection are also restrained into a certain region, respectively. Numerical results are provided to illustrate the effectiveness of the proposed controllers.