Finite-Time Boundary Output Feedback Stabilization of an Anti-Stable Wave Equation With Matched Disturbance

This paper addresses the finite-time output feedback stabilization of an anti-stable wave equation under boundary control with matched disturbance. A framework combining sliding mode control (SMC) and backstepping is proposed, in which a finite-time state-feedback controller is first designed. Using the Galerkin method and successive approximation technique, the existence of the generalized solution for the closed-loop system is established. Moreover, the selected sliding mode surface ensures finite-time convergence of system states to zero along the manifold. Subsequently, an observer-based output feedback controller is constructed to eliminate the dependence on full-state measurements. Finally, the numerical simulations validate the theoretical results.