Boundary stabilization and matched disturbance rejection of hyperbolic PDE systems: A sliding-mode approach

This paper deals with the robust boundary stabilization problem of hyperbolic partial differential equations (PDEs) subject to boundary uncertainties. These systems include a second-order undamped wave equation and a first-order delay system. By taking the integral transformation, we obtain a nominal PDE with asymptotic stability in the new coordinates when an appropriate boundary control input is applied. The associated Lyapunov function can then be used for designing an infinite-dimensional sliding surface, on which the system exhibits exponential stability, invariant of the bounded matched disturbance. A continuous sliding-mode boundary control law satisfied with reaching condition is employed to ensure the system's will reach the proposed sliding surface within finite time. Simulation results of a second-order wave equation are provided to demonstrate and compare with the other control schemes.