Integral Action Feedback Design for Conservative Abstract Systems in the Presence of Input Nonlinearities

In this article, we present a stabilization feedback law with integral action for conservative abstract linear systems subjected to input nonlinearities. Based on the designed control law, we first prove the well-posedness using nonlinear semigroups theory and global asymptotic stability of the origin for the closed-loop system by constructing a weak Lyapunov functional. Secondly, as an illustration, we apply the results to a wave equation with integral action in two different cases: bounded control operator and unbounded control operator.