Stabilization for infinite-dimensional linear systems with bounded control and time delayed observation

For a practical control system, there is most often a time delay between the controller to be implemented and the information via the observation of the system. The time delay suffered from observation presents a mathematical challenge in output feedback stabilization for linear infinite-dimensional systems because the time delay may destroy the stability. This drives us to re-design stabilizing controller in the presence of time delay. In this paper, based on our previous work, we develop a stabilizing controller for systems with bounded linear control operators by observer based output feedback in the time interval where the observation is available and the predictor where the observation is not available. The result is applied to the stabilization of the several partial differential equation control systems with time delay in observations.