Title: Output feedback exponential stabilization for 1-D unstable wave equations with boundary control matched disturbance,
Abstract: We study the output feedback exponential stabilization of a one-dimensional
unstable wave equation, where the boundary input, given by the Neumann trace at
one end of the domain, is the sum of the control input and the total
disturbance. The latter is composed of a nonlinear uncertain feedback term and
an external bounded disturbance. Using the two boundary displacements as output
signals, we design a disturbance estimator that does not use high gain. It is
shown that the disturbance estimator can estimate the total disturbance in the
sense that the estimation error signal is in $L^2[0,\infty)$. Using the
estimated total disturbance, we design an observer whose state is exponentially
convergent to the state of original system. Finally, we design an
observer-based output feedback stabilizing controller. The total disturbance is
approximately canceled in the feedback loop by its estimate. The closed-loop
system is shown to be exponentially stable while guaranteeing that all the
internal signals are uniformly bounded.