Boundary control for a vibrating string with asymmetrical constrained outputs

In this paper, the flexible string system with the boundary disturbance is modeled as a homogeneous partial differential equation and two ordinary differential equations. A boundary controller is designed to suppress the undesirable vibrations for the flexible string system, where the tangent functions are introduced into the barrier Lyapunov function to guarantee the output constrained asymmetrically. The closed-loop system is therefore stabilized asymptotically and even the uniform boundedness is achieved. Simulation results are aimed to prove the effectiveness of the boundary control.